Numerical Methods & Mathematical Analysis 2
Bachelor in Electrical and Computers Engineering
Photo credits @historiasdeencantar.pt
Bio
I am currently a Doctorate Auxiliary Researcher and Lecturer at the Faculty of Engineering of the University of Porto and I have been developing my work in the areas of optimal control and model predictive control having a particular interest in nonlinear and constrained problems.
Continuing my Ph.D. research, I am interested in increasing the accuracy of numerical solutions of optimal control problems obtained via direct methods, mainly by developing fast adaptive time-mesh refinement algorithms. I am also interested in optimal control applications, namely in the energy, robotics, and health fields.
Recent Academic Positions
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2022 Present
Doctorate Auxiliary Researcher
DEEC, Faculty of Engineering, University of Porto, Porto
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2019 Present
Lecturer
DEEC, Faculty of Engineering, University of Porto, Porto
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2021 2022
Invited Lecturer
ISEP, School of Engineering, Polytechnic of Porto, Porto
Academic Education
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2014 Ph.D.
Applied Mathematics
University of Porto, Faculty of Science, Porto
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2004 M.Sc.
Computer Methods for Sciences & Engineering
University of Porto, Faculty of Science, Porto
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2002 First degree
Applied Mathematics
University of Porto, Faculty of Science, Porto
Awards, Honors and Grants
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June 2021Best Presentation AwardComparison of L0 and L1 path-following controllers for Airborne Wind Energy Systems
S. Vinha, L.T. Paiva, F.A.C.C. Fontes
DCE’21 - 4th Doctoral Congress in Engineering: Symposium on Electrical and Computing Engineering (online) -
July 2019Best Presentation AwardLayout Optimization of an AWE Farm for Maximum Power Generation
L.A.C. Roque, L.T. Paiva, M.C.R.M. Fernandes, D.B.M.M. Fontes, F.A.C.C. Fontes
6th International Conference On Energy and Environment Research, Aveiro -
July 2017Best Paper AwardOptimal Control of Underwater Kite Power Systems
Luís Tiago Paiva, F.A.C.C. Fontes
International Conference in Engineering Applications, Funchal -
March 2017FCT Post-doctoral FellowshipGlobal Optimisation-based Control of Hybrid Systems
Ref.: SFRH/BPD/126683/2016
Faculty of Engineering, University of Porto, Porto, Portugal
Supervision
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2023-todayAutonomous Vehicle Racing - Digital TwinDuarte Lima Silva
Master in Electrical and Computers Engineering (supervisor)
University of Porto, Faculty of Engineering, PortoSmart Manufacturing in the semiconductor industry: Cognitive Assistant for a Digital TwinAmélia Beatriz de Castro Machado
Master in Electrical and Computers Engineering (co‐supervisor)
University of Porto, Faculty of Engineering, PortoUPWIND - Otimização da Energia num Ciclo Completo de Produção de Sistemas Aéreos de Energia EólicaEduardo Cabral Martins Barbosa
Master in Electrical and Computers Engineering (co‐supervisor)
University of Porto, Faculty of Engineering, PortoDescolagem e Aterragem de Asas Autónomas em Sistemas Aéreos de Energia EólicaAna Rita Reimão Couto
em>Master in Electrical and Computers Engineering (co‐supervisor)
University of Porto, Faculty of Engineering, Porto -
2022-2023Layout Optimisation and Power Averaging of an Airborne Wind Energy FarmRui Carvalho da Costa
Master in Electrical and Computers Engineering (supervisor)
University of Porto, Faculty of Engineering, PortoTake-off and Landing of Autonomous Flying Wings in Airborne Wind Energy SystemsGabriel Moura Fernandes
Master in Electrical and Computers Engineering (co‐supervisor)
University of Porto, Faculty of Engineering, Porto -
2021-TodayUPWIND - Optimização de Trajetórias de Asas Autónomas em Sistemas Aéreos de Energia Eólica (AWES)André Rodrigues Ribeiro
Master in Electrical and Computers Engineering (co‐supervisor)
University of Porto, Faculty of Engineering, PortoViabilidade económica da tecnologia Airborne Wind Energy Systems (AWES)João Correia
Master in Electrical Engineering (co‐supervisor)
Polytechnique of Porto, School of Engineering, Porto -
2019-2020Emerging renewable energy technologies: Survey, modeling, and simulationsOctávio Ferreira
Master in Electrical Engineering (co‐supervisor)
Polytechnique of Porto, School of Engineering, PortoAproveitamento Eólico em Centrais Hídricas Equipadas com BombagemEduardo Salgado
Master in Electrical Engineering (co‐supervisor)
Polytechnique of Porto, School of Engineering, Porto -
2018-2019Indoor Tracking for DronesSérgio Vinha
Master in Electrical and Computers Engineering (co‐supervisor)
University of Porto, Faculty of Engineering, PortoDeterminação do Benefício Económico de Centrais Hídricas Equipadas com Bombagem no Aproveitamento ÉolicoAntónio Mendes
Master in Electrical Engineering (co‐supervisor)
Polytechnique of Porto, School of Engineering, Porto -
2017-2018Airborne Wind Energy Systems: Modelling, Simulation and Trajectory ControlGonçalo Silva
Master in Electrical and Computers Engineering (co‐supervisor)
University of Porto, Faculty of Engineering, PortoAirborne Wind Energy Systems: Modelling, Simulation and Economic AnalysisManuel Fernandes
Master in Electrical and Computers Engineering (co‐supervisor)
University of Porto, Faculty of Engineering, Porto -
2013-2014Optimal Control of Power Kites for Wind Power ProductionTiago Costa Moreira Maia
Master in Electrical and Computers Engineering (co‐supervisor)
University of Porto, Faculty of Engineering, Porto
Teaching
Current Teaching
Invited Lecturer
Department of Electrical and Computers Engineering, Faculty of Engineering, University of Porto, Porto
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2023 Present
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2022 2023
Numerical Methods & Probability and Statistics
Bachelor in Electrical and Computers Engineering
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2021 2022
Numerical Methods
Bachelor in Electrical and Computers Engineering
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2020 2021
Numerical Methods
Master degree in Electrical and Computers Engineering
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2019 2020
Numerical Methods
Master degree in Electrical and Computers Engineering
Teaching History
Invited Lecturer
Department of Mathematics, School of Engineering, Polytechnic of Porto, Porto
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2021 2022
Discrete Mathematics
First degree in Informatics Engineering
Invited Lecturer
School of Economics and Management, University of Porto, Porto
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2020 2021
Project Management
Master degree in Management
Invited Lecturer
Department of Mathematics, School of Engineering, Polytechnic of Porto, Porto
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2016 2017
Mathematics 1
First degree in Automotive Engineering
Assistant Lecturer
Faculty of Science and Technology, University Fernando Pessoa, Porto
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2011 2012
Numerical Analysis
First degree in Civil Engineering, Computer Engineering, Environmental Engineering, Engineering and Quality Management
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2010 2011
Numerical Analysis¹ & Foundations of Mathematics²
¹First degree in Civil Engineering, Computer Engineering, Environmental Engineering, Engineering and Quality Management
²First degree in Business Sciences -
2009 2010
Numerical Analysis¹, Analysis 2¹ & Foundations of Mathematics²
¹First degree in Civil Engineering, Computer Engineering, Environmental Engineering, Engineering and Quality Management
²First degree in Business Sciences -
2008 2009
Numerical Analysis
First degree in Civil Engineering, Computer Engineering, Environmental Engineering, Engineering and Quality Management
Teaching Assistant
Department of Mathematics, Faculty of Sciences, University of Porto, Porto
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2005 2006
Calculus
First degree in Physics
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2004 2005
Numerical Analysis 1¹, Numerical Analysis 2² & Calculus³
¹First degree in Mathematics
²First degree in Applied Mathematics and Mathematics Applied to Technology
³First degree in Physics -
2003 2004
Numerical Analysis 2¹ & Calculus²
¹First degree in Applied Mathematics and Mathematics Applied to Technology
²First degree in Physics
Research Summary
I am currently a Postdoctoral Research Associate at the University of Porto and I have been developing my work in the areas of optimal control and model predictive control having a particular interest in nonlinear and constrained problems.
Continuing my Ph.D. research, I am interested in increasing the accuracy of numerical solutions of optimal control problems obtained via direct methods, mainly by developing adaptive time-mesh refinement algorithms.
I am also interested in optimal control applications, namely in the energy, robotics, and health fields.
- Optimal Control
- Model Predictive Control
- Kite Power Systems
- Infection Control
- Numerical Analysis
Research Projects
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2023-TodayA Multi-Kite System to Harvest High Altitude Wind PowerUPWIND - A Multi-Kite System to Harvest High Altitude Wind Power
Ref.: 2022.02801.PTDC
Researcher (20%) -
2023-TodayDesign and Optimisation Algorithms for Kite Wind Energy FarmsKEFCODE – Design and Optimisation Algorithms for Kite Wind Energy Farms
Ref.: 2022.02320.PTDC
Researcher (15%) -
2017-2022Distributed Optimal Control for Cyber-Physical Systems ApplicationsHARMONY - Distributed Optimal Control for Cyber-Physical Systems Applications
Ref.: PTDC/EEI-AUT/31411/2017
Researcher (20%) -
2017-2022Multi-Agent Control and Estimation for Multi-Horizon Goals ConciliationMAGIC – Multi-Agent Control and Estimation for Multi-Horizon Goals Conciliation
Ref.: PTDC/EEI-AUT/32485/2017
Researcher (15%) -
2017-2022The Optimal Challenges in IrrigationTO CHAIR - The Optimal Challenges in Irrigation
Ref.: PTDC/MAT-APL/28247/2017
Researcher (15%) -
2017-2022A Multi-Kite System to Harvest High Altitude Wind PowerUPWIND - A Multi-Kite System to Harvest High Altitude Wind Power
Ref.: PTDC/EEI-AUT/31447/2017
Researcher (30%) -
2017-2021Global Optimisation-based Control of Hybrid SystemsGlobal Optimisation-based Control of Hybrid Systems
Ref.: SFRH/BPD/126683/2016
FCT Post-doctoral Fellow (100%) -
2016-2019Theory, Applications and Numerics of Optimal ControlTOCCATA - Teoria, Aplicações e Computação Numérica de Controlo Ótimo
Ref.: PTDC/EEI‐AUT/2933/2014
Researcher (30%) -
2015-2016Research Center for Systems and TechnologiesSYSTEC - Research Center for Systems and Technologies
Ref.: POCI-01-0145-FEDER-006933
Postdoctoral Research Associate (100%) -
2015Smart Manufacturing and LogisticsProdução e Logística Inteligentes
Ref.: NORTE-07-0124-FEDER-000057
Postdoctoral Research Associate (100%) -
2014-2015Research Center for Systems and TechnologiesSYSTEC - Research Center for Systems and Technologies
Ref.: INCENTIVO/EEI/UI0147/2014
Grant-holding Researcher (100%) -
2014Smart Forecast Systems for Energy and Water ManagementSMART4CAST - Sistemas Inteligentes de Previsão para Gestão de Energia e Água
Ref.: FEUP/SMARTWATT/2014
Researcher (15%) -
2014Optimal Control: Health, Energy and Robotics ApplicationsOCHERA - Controlo Óptimo: Aplicações em Saúde, Energia e Robótica
Ref.: PTDC/EEI-AUT/1450/2012
Grant-holding Researcher (100%) -
2012-2013Optimal Control for Constrained, Nonlinear & Hybrid SystemsOCCOHyNS - Controlo Óptimo em Sistemas Não Lineares Híbridos e com Restrições
Ref.: PTDC/EEA-CRO/116014/2009
Grant-holding Researcher (100%) -
2009-2011High Performance Computing of Wind Over Complex TerrainCOMPWIND - Computação de elevado desempenho do vento sobre terreno complexo
Ref.: PTDC/ENR/71216/2006
Grant-holding Researcher (100%) -
2007-2008Seismic Risk and Tsunamis in the AlgarveERSTA - Estudo do risco sismico e de tsunamis do Algarve
Ref.: IME/AUR/49901/2003
Grant-holding Researcher (100%) -
2004-2005Urban Planning for Immigrant IntegrationPlaneamento Urbano para a Integração de Imigrantes
Ref.: IME/AUR/49901/2003
Grant-holding Researcher (100%)
Research Work
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Software: ICLOCS, AMPL, IPOPT, Matlab.
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Software: ICLOCS, AMPL, BOCOP, IPOPT, KNITRO, Matlab.
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Main responsibilities: To develop a framework for the control of Hybrid Systems through Optimization-based Control techniques, which use Global Optimization Methods, namely: (a) to develop or select an appropriate framework to model and simulate hybrid systems; (b) to develop and/or adapt Optimal Control and Model Predictive Control techniques to the context of our hybrid systems framework; (c) to develop and/or adapt Global Optimization algorithms to be used in optimization-based control techniques; (d) to apply the developed techniques to problems in the areas of robotics, automotive systems, power systems, health and the environment.
Software: ICLOCS, AMPL, BOCOP, IPOPT, KNITRO, Matlab.
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Main responsibilities: To build and maintain a software platform to test and illustrate the use of the conceptual tools developed during the overall project: not only in academic examples but also in case studies in the areas of robotics, medicine and exploitation of renewable resources.
Software: Matlab, ICLOCS, AMPL, IPOPT.
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Main responsibilities: To collaborate on the development of forecasting system of wind-based electric power encompassing physical and statistical models with intel from different fields, such as meteorological forecasting, simulation of complex meso and micro-scale flows, operational data of wind-farms and of the grid.
Software: Matlab, OpenFOAM, PARAMESH, Tecplot, VENTOS.
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Main responsibilities: To model the pattern of tectonic stress in the Algarve shore, using finite element methods in 2D and 3D. To determine the rheological stratification of the lithosphere in the Gulf of Cadiz and adjacent region and to develop models of mechanical behavior of the lithosphere to identify areas of accumulation of stress that can generate earthquakes.
Main results: We built a 3D model of faults of the Gulf of Cadiz. We developed a new graphic software to analyze the potential for displacement faults.
Software: Matlab, COULOMB, Mirone, GiD, CUBIT, Pylith.
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Main responsibilities: To develop an automated procedure to detect significant changes in several time series to be included in a Network Intelligence System for decision support that identifies and monitors market opportunities. Data: EUROSTAT.
Main results: We designed and implemented PHP algorithms which analyse data, estimate the best model as well as prediction bands, achieving results in a quickly and efficiently way. The company got a new highly innovative product aimed to detect areas of opportunity and to support decisions that generate profitable realities and optimised costs.
Software: SPSS, R. MySQL with PHP.
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Main responsibilities: To develop a toolbox for orthogonal polynomials and their characterizations, generalizations and applications. To develop all the documentation that supports the toolbox.
Main results: We implemented a new add-on for Mathematica, including a user manual, which was presented at the Wolfram Technology Conference 2005 by invitation of Wolfram Research. We started conversations for a partnership with Wolfram Research. I became alpha / beta tester of the new versions of Mathematica.
Software: Mathematica.
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Main responsibilities: To develop activities for collecting and processing information and operating Neural Networks and Geographic Information Systems. Data: CENSOS2001.
Main results: We developed decision trees to determine the ideal parishes and municipalities of residence and work for immigrants in the Porto Metropolitan Area (AMP). All immigrant communities of AMP were characterized in detail. This work was published by the High Commissioner for Immigration and Ethnic Minorities.
Software: MatLab, SPSS, ArcView.
Publications
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L0 and L1 Guidance and Path–Following Control for Airborne Wind Energy Systems
Journal Paper in Energies, 15 (4), 1390, February 2022.
Abstract
Layout optimization of an airborne wind energy farm for maximum power generation
Journal Paper in Energy Reports, 6 (1), pp. 165–171, February 2020.
Abstract
We consider a farm of Kite Power Systems (KPS) in the field of Airborne Wind Energy (AWE), in which each kite is connected to an electric ground generator by a tether. In particular, we address the problem of selecting the best layout of such farm in a given land area such that the total electrical power generated is maximized. The kites, typically, fly at high altitudes, sweep a greater area than that of traditional wind turbines, and move within a conic shaped volume with vertex on the ground station. Therefore, constraints concerning kite collision avoidance and terrain boundaries must be considered. The efficient use of a given land area by a set of KPS depends on the location of each unit, on its tether length and on the elevation angle. In this work, we formulate the KPS farm layout optimization problem. Considering a specific KPS and wind characteristics of the given location, we study the power curve as a function of the tether length and elevation angle. Combining these results with an area with specified length and width, we develop and implement a heuristic optimization procedure to devise the layout of a KPS farm that maximizes wind power generation.
A Path–following Guidance Method for Airborne Wind Energy Systems with Large Domain of Attraction
Conference Paper in ACC’19 Proceedings – 2019 American Control Conference, IEEE, pp. 2771–2776, July 2019.
Abstract
We address the problem of generating electrical power through Airborne Wind Energy Systems, using a kite connected to a generator on the ground. We propose a controller to steer the kite to follow a pre-defined eight-shaped path based on a nonlinear guidance logic. The controller has an easy implementable explicit form, has asymptotic stability guarantees and a large domain of attraction. We report simulations of a complete production cycle, including a production phase and a recovery phase. Also, we provide a Lyapunov stability analysis.
Sampled–data Model Predictive Control: Adaptive Time–mesh Refinement Algorithms and Guarantees of Stability
Journal Paper Discrete and Continuous Dynamical Systems, 24 (5), pp. 2335–2364, May 2019.
Abstract
This article addresses the problem of controlling a constrained, continuous-time, nonlinear system through Model Predictive Control (MPC). In particular, we focus on methods to efficiently and accurately solve the underlying optimal control problem (OCP). In the numerical solution of a nonlinear OCP, some form of discretization must be used at some stage. There are, however, benefits in postponing the discretization process and maintain a continuous-time model until a later stage. This is because that way we can exploit additional freedom to select the number and the location of the discretization node points. We propose an adaptive time-mesh refinement (AMR) algorithm that iteratively finds an adequate time-mesh satisfying a pre-defined bound on the local error estimate of the obtained trajectories. The algorithm provides a time-dependent stopping criterion, enabling us to impose higher accuracy in the initial parts of the receding horizon, which are more relevant to MPC. Additionally, we analyze the conditions to guarantee closed-loop stability of the MPC framework using the AMR algorithm. The numerical results show that the proposed AMR strategy can obtain solutions as fast as methods using a coarse equidistant-spaced mesh and, on the other hand, as accurate as methods using a fine equidistant-spaced mesh. Therefore, the OCP can be solved, and the MPC law obtained, faster and/or more accurately than with discrete-time MPC schemes using equidistant-spaced meshes.
Guaranteed Constraint Satisfaction in Continuous–Time Control Problems
Journal Paper IEEE Control Systems Letters, 3 (1), pp. 13–18, January 2019 | doi: 10.1109/LCSYS.2018.2849853
Abstract
In the context of continuous-time control systems, we address the problem of guaranteeing that the constraints imposed along the trajectory are in fact satisfied for all times. The problem is relevant and non-trivial in situations in which a continuous-time internal representation of the system is used with a digital device, such as in sampled-data model-based control, in an optimal control solver, or in sampled-data model predictive control. In this letter, we establish a condition that when verified on a finite set of time instants (using limited computational power) can guarantee that the trajectory constraints are satisfied on an uncountable set of times. The case of constrained optimal control problems is further explored here. We develop an algorithm for the numerical solution of constrained nonlinear optimal control problems that combines a guaranteed constraint satisfaction strategy with an adaptive mesh refinement strategy.
Optimal Electrical Power Generation with Underwater Kite Systems
Journal Paper Computing, 100 (11), pp. 1137–1153, November 2018. | doi: 10.1007/s00607-018-0643-4
Abstract
In this article we investigate the problem of generating electricity through an underwater kite power system (UKPS). For this problem, we develop the dynamical model for the UKPS and we formulate an optimal control problem to devise the trajectories and controls of the kite that maximize the total energy produced in a given time interval. This is a highly nonlinear problem for which the optimization is challenging. We also develop a numerical solution scheme for the optimal control problem based on direct methods and on adaptive time-mesh refinement. We report results that show that the problem can be quickly solved with a high level of accuracy when using our adaptive mesh refinement strategy. The results provide a set of output power values for different design choices and confirm that electrical energy that can be produced with such device.
A Sufficient Condition for Stability of Sampled–data Model Predictive Control using Adaptive Time–mesh Refinement
Conference Paper in IFAC-PapersOnLine, 51 (20), pp. 104–109, August 2018.
Abstract
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A Trajectory Controller for Kite Power Systems with Wind Gust Handling Capabilities
Conference Paper in ICINCO’18 Proceedings – 15th International Conference on Informatics in Control, Automation and Robotics, SCITEPRESS – Science and Technology Publications, pp. 533–540, July 2018.
Abstract
In this paper, we address the generation of electrical power using Airborne Wind Energy Systems, comprising a kite connected through a tether to a generator on the ground. We design a controller to steer the kite to follow a pre-defined periodic path, which includes a production mode, a tether retrieval mode, and a safe mode capable of handling wind gusts.
Optimal Reorganization of a Formation of Nonholonomic Agents Using Shortest Paths
Conference Paper in in CONTROLO’18 Proceedings – 13th APCA International Con- ference on Control and Soft Computing, IEEE, pp. 177–182, June 2018.
Abstract
In this work we address the problem of switching the shape of a formation of undistinguishable nonholonomic mobile robots. Each agent moves from the current to its target oriented position using the shortest path. We combine results from previous work on optimal formation switching when the agents are holonomic with results on the structure of the shortest path for nonholonomic agents.
Optimal Control Algorithms with Adaptive Time–Mesh Refinement for Kite Power Systems
Journal Paper Energies, 11(3):475, pp. 1-17, February 2018 | doi: 10.3390/en11030475
Abstract
This article addresses the problem of optimizing electrical power generation using kite power systems (KPSs). KPSs are airborne wind energy systems that aim to harvest the power of strong and steady high-altitude winds. With the aim of maximizing the total energy produced in a given time interval, we numerically solve an optimal control problem and thereby obtain trajectories and controls for kites. Efficiently solving these optimal control problems is crucial when the results are used in real-time control schemes, such as model predictive control. For this highly nonlinear problem, we derive continuous-time models — in 2D and 3D —a nd implement an adaptive time-mesh refinement algorithm. By solving the optimal control problem with such an adaptive refinement strategy, we generate a block-structured adapted mesh which gives results as accurate as those computed using fine mesh, yet with much less computing effort and high savings in memory and computing time.
Optimal control of kite power systems: mesh–refinement strategies
Conference Paper Energy Procedia, 136, pp. 302-307, October 2017 | doi: 10.1016/j.egypro.2017.10.254
Abstract
In this work we address the problem of generating electricity through Kite Power Systems. We solve an optimal control problem which devises the trajectories and controls for the kite that maximize the total energy produced in a given interval. This is a highly nonlinear problem for which the optimization is challenging. We use a continuous–time model of the kite and implement time mesh–refinement strategies to solve the problem. We report results that show that with an adaptive mesh refinement strategy the problem can be solved with a high level of accuracy and (in simplified versions) much faster.
Optimal control of underwater kite power systems
Conference Paper in 2017 International Conference in Energy and Sustainability in Small Developing Economies (ES2DE) Proceedings, pp. 1-6, July 2017 | doi: 10.1109/ES2DE.2017.8015353
Abstract
We address the problem of generating electricity through Underwater Kite Power Systems. For this problem, we develop an optimal control problem formulation using a continuous-time model of the kite to devise the trajectories and controls for the kite that maximize the total energy produced in a given time interval. This is an highly nonlinear problem for which the optimization is challenging. We also develop a numerical solution scheme for the optimal control problem based on direct methods and on adaptive time-mesh refinement. We report results that show that the problem can be quickly solved with a high level of accuracy when using our adaptive mesh refinement strategy. The results confirm the values of electrical power that can be produced with such device.
Optimization–based control of constrained nonlinear systems with continuous–time models: Adaptive time–grid refinement algorithms
Conference Paper in AIP Conference Proceedings, 1776 (1), pp. 090009_1-090009_5, October 2016 | doi: 10.1063/1.4965373
Abstract
We address optimal control problems for nonlinear systems with pathwise state-constraints. These are challenging non-linear problems for which the number of discretization points is a major factor determining the computational time. Also, the location of these points has a major impact in the accuracy of the solutions. We propose an algorithm that iteratively finds an adequate time-grid to satisfy some predefined error estimate on the obtained trajectories, which is guided by information on the adjoint multipliers. The obtained results show a highly favorable comparison against the traditional equidistant–spaced time–grid methods, including the ones using discrete–time models. This way, continuous–time plant models can be directly used. The discretization procedure can be automated and there is no need to select a priori the adequate time step. Even if the optimization procedure is forced to stop in an early stage, as might be the case in real-time problems, we can still obtain a meaningful solution, although it might be a less accurate one. The extension of the procedure to a Model Predictive Control (MPC) context is proposed here. By defining a time–dependent accuracy threshold, we can generate solutions that are more accurate in the initial parts of the receding horizon, which are the most relevant for MPC.
Sampled-Data Model Predictive Control Using Adaptive Time-Mesh Refinement Algorithms
Book Chapter in Lecture Notes in Electrical Engineering, 402, pp. 143-153, September 2016 | doi: 10.1007/978-3-319-43671-5_13
Abstract
We address sampled-data nonlinear Model Predictive Control (MPC) schemes, in particular we address methods to efficiently and accurately solve the underlying continuous-time optimal control problems (OCP). In nonlinear OCPs, the number of discretization points is a major factor affecting the computational time. Also, the location of these points is a major factor affecting the accuracy of the solutions. We propose the use of an algorithm that iteratively finds the adequate time–mesh to satisfy some pre–defined error estimate on the obtained trajectories. The proposed adaptive time–mesh refinement algorithm provides local mesh resolution considering a time–dependent stopping criterion, enabling an higher accuracy in the initial parts of the receding horizon, which are more relevant to MPC. The results show the advantage of the proposed adaptive mesh strategy, which leads to results obtained approximately as fast as the ones given by a coarse equidistant–spaced mesh and as accurate as the ones given by a fine equidistant–spaced mesh.
Reference Tracking of Depth of Anesthesia Using Optimal Control
Conference Paper in SIAM Conference on Control and Its Applications, pp. 356-360, July 2015 | doi: 10.1137/1.9781611974072.49
Abstract
Optimal control theory has gained increasing importance in biomedical applications, e.g., in the automatic administration of anesthetics during general anesthesia. One example of a monitored state is the depth of anesthesia, which is usually achieved by the joint administration of hypnotics and analgesics. This state is quantified by the bispectral index that varies between 97.7% and 0%. On the other hand, the amount of drug to be administered should be optimized both for patient health and for economical reasons. This motivates the use of optimal control in this field of application. In this contribution, a static state--feedback control law is considered. In order to determine a suitable feedback gain, a nonlinear optimal control problem is formulated and solved using direct methods. These methods have become increasingly useful when computing the numerical solution of an optimal control problem. Moreover, they are known to provide a very robust and general approach.
An Optimal Control Approach to Reference Level Tracking in General Anesthesia
Conference Paper in Mediterranean Conference on Control and Automation, pp. 124-129, June 2015 | doi: 10.1109/MED.2015.7158739
Abstract
In this paper the neuromuscular blockade level and the bispectral index level tracking problems by means of automatic control are considered in the context of general anesthesia. These tracking problems are formulated as optimal control problems that are numerically solved using direct methods. The results shown in this paper are preliminaries but illustrates a good performance of this strategy when applied to biomedical problems.
Adaptive Time-Mesh Refinement in Optimal Control Problems With State Constraints
Journal Paper Discrete and Continuous Dynamical Systems, 35 (9), pp. 4553-4572, September 2015 | doi: 10.3934/dcds.2015.35.4553
Abstract
When using direct methods to solve nonlinear optimal control, regular time meshes having equidistant spacing are most frequently used. However, in some cases, these meshes cannot cope accurately with nonlinear behaviour and increasing uniformly the number of mesh nodes may lead to a more complex problem, resulting in an incoherent solution. We propose an adaptive time--mesh refinement algorithm, considering different levels of refinement and several mesh refinement criteria. This technique is applied to solve an optimal control problem involving nonholonomic vehicles with state constraints which is characterized by presenting strong nonlinearities and by having discontinuous controls. The presented strategy leads to results with higher accuracy and yet with lower overall computational time, when compared to results obtained by meshes having equidistant spacing. In addition, the algorithm was able to obtain a solution when the traditional approach starting with a very large number of mesh nodes failed to do it, proving its robustness. Afterwards, we apply the necessary condition of optimality in the form of the Maximum Principle of Pontryagin to characterize the solution and to validate the numerical results.
Numerical Methods in Optimal Control and Model Predictive Control
Thesis PhD Thesis, Universidade do Porto, 2014
Abstract
This thesis addresses, via numerical and optimisation methods, the control of nonlinear systems whose inputs or trajectories are subject to constraints. Nevertheless, we review and apply theoretical results, such as conditions of optimality, to characterise the optimal trajectory and to validate numerical results obtained using our proposed methods. We overview most used software packages for solving optimal control problems, including numerical solvers which invoke local search methods and interfaces with distinct features. A benchmark involving a differential drive robot with state constraints is presented in order to compare the performances of the solvers. We propose and develop an optimal control algorithm based on a direct method with adaptive refinement of the time--mesh. When using direct methods to solve nonlinear optimal control, regular time meshes having equidistant spacing are most frequently used. However, in some cases, these meshes cannot cope accurately with nonlinear behaviour and increasing uniformly the number of mesh nodes may lead to a more complex problem, resulting in an incoherent solution. We propose a new adaptive time--mesh refinement algorithm, considering different levels of refinement and several mesh refinement criteria. This technique is applied to solve an open--loop optimal control problem involving nonholonomic vehicles with state constraints, which is characterized by presenting strong nonlinearities and by having discontinuous controls, and a compartmental model for the implementation of a vaccination strategy. This algorithm leads to results with higher accuracy and yet with lower overall computational time, when compared to results obtained by meshes having equidistant--spacing. We extend the time--mesh refinement algorithm to be applied to a sequence of optimal control problems in a Model Predictive Control scheme. Model Predictive Control is a technique widely used in industrial control problems that explicitly consider constraints. The receding horizon control strategy can be used in real time applications and it can be implemented for large-scale systems. The proposed algorithm is applied to solve an optimal control problem involving parking manoeuvres. The results are obtained as fast as the ones given by a coarse equidistant--spacing mesh and as accurate as the ones given by a fine equidistant--spacing mesh. Global Optimisation methods are addressed as well. The accurate solution of optimal control is crucial in many areas of engineering and applied science. Since problems involving nonlinear systems often contain multiple local minima, we study deterministic and heuristic methods which attempt to determine the global solution. A problem involving a car--like system is successfully solved and the global optimum is found.
Time-Mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles
Conference Paper in Procedia Technology, 17, pp. 178-185, December 2014 | doi:10.1016/j.protcy.2014.10.226
Abstract
Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are most frequently used. However, in some cases, these meshes cannot cope accurately with nonlinear behaviour unless a very large number of mesh nodes is used. One way to improve the solution involves adaptive mesh refinement algorithms which allow a non uniform node collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. The technique was applied to solve two problems involving nonholonomic vehicles and it led to results with higher accuracy and yet with lower overall computational time when compared to a mesh having equidistant nodes.
Introducing State Constraints in Optimal Control for Health Problems
Conference Paper in Procedia Technology, 17, pp. 415-422, December 2014 | doi:10.1016/j.protcy.2014.10.249
Abstract
An optimal control problem with state constraints based on a SEIR model to control the spreading of infectious diseases is considered. The main purpose is apply novel theoretical results to successfully validate the numerical solution, computed via direct method. The problem has simple but yet interesting features that we explore in our analysis. Of particular interest is the fact that the state constraint is of order one and that the solution is normal.
Determining wind turbine power curves based on operating conditions
Journal Paper Wind Energy, 17 (10), pp. 1563–1575, October 2014 | doi: 10.1002/we.1651
Abstract
The relation between wind speed and electrical power—the power curve—is essential in the design, management and power forecasting of a wind farm. The power curve is the main characteristic of a wind turbine, and a procedure is presented for its determination, after the wind turbine is installed and in operation. The procedure is based on both computational and statistical techniques, in situ measurements, nacelle anemometry and operational data. This can be an alternative or a complement to procedures fully based on field measurements as in the International Electrotechnical Commission standards, reducing the time and costs of such practices. The impact of a more accurate power curve was measured in terms of the prediction error of a wind power forecasting system over 1 year of operation, whereby the methodology for numerical site calibration was presented and the concepts of ideal power curve and nacelle power curve introduced. The validation was based on data from wind turbines installed at a wind farm in complex topography, in Portugal, providing a real test of the technique presented here. The contribution of the power curve to the wind power forecasting uncertainty was found to be from 10% to 15% of the root mean square error.
A SEIR Model for Control of Infectious Diseases with Constraints
Journal Paper Mathematical Biosciences and Engineering, 11 (4), pp. 761-784, August 2014 | doi: 10.3934/mbe.2014.11.761
Abstract
Optimal control can be of help to test and compare different vaccination strategies of a certain disease. In this paper we propose the introduction of constraints involving state variables on an optimal control problem applied to a compartmental SEIR (Susceptible, Exposed, Infectious and Recovered) model. We study the solution of such problems when mixed state control constraints are used to impose upper bounds on the available vaccines at each instant of time. We also explore the possibility of imposing upper bounds on the number of susceptible individuals with and without limitations on the number of vaccines available. In the case of mere mixed constraints a numerical and analytical study is conducted while in the other two situations only numerical results are presented.
Mesh refinement strategy for optimal control problems
Conference Paper in AIP Conference Proceedings, 1558 (1), pp. 590-593, October 2013 | doi: 10.1063/1.4825560
Abstract
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Optimal Control for Constrained Hybrid System: Computational Libraries and Applications
Technical Report Universidade do Porto, February 2013.
Abstract
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Analysis of the Similarity in Turbulence Intensity and Wind Shear as Function of the Wind Velocity: Field Measurements and Numerical Results
Conference Paper in European Wind Energy Conference and Exhibition 2010, EWEC 2010, 4, pp. 2742-2788, Varsaw, Poland, April 2010.
Abstract
...
Software for slip-tendency analysis in 3D: A plug-in for Coulomb
Journal Paper Computers and Geosciences, 35 (12), pp. 2345-2352, December 2009 | doi: 10.1016/j.cageo.2009.03.008
Abstract
Slip-tendency analysis is a valuable tool in fault reactivation evaluation and seismic hazard assessment as it provides a means of quantifying the slip potential on mapped or suspected faults in a known or inferred stress field. We developed an interactive graphic tool to perform slip-tendency analysis. The application is written in MATLAB in the form of plug-ins for COULOMB, a graphic-rich deformation and stress change open-source software. In addition to identifying the faults most prone to reactivation, we compute and plot synthetic focal mechanisms from the direction and sense of likely slip. This allows compatibility between focal mechanisms and geological structures to be verified. Both individual faults and fault networks can be considered in three dimensions. The potential for slip depends on the prevailing stress field, the fault surface orientation and the coefficient of friction. These parameters are given interactively in a Windows environment. The application thus offers an easy-to-use graphical interface with the possibility of fast parameter modification and 3D visualization of the results.
A New Graphical Software Tool To Analyze The Slip Potential Of Faults
Conference Paper in 6th Portuguese and Spanish Assembly of Geodesy and Geophysics, pp. 456-467, Tomar, Portugal, February 2008.
Abstract
...
Urban Planning for Immigrants Integration
Book Chapter in Getting to know more, so as to act better, Portuguese Immigration Observatory, pp. 109-120, October 2006.
In legal terms, the bases of spatial planning and urbanism policy are laid out in law no 48/98, of 11th August, where it states that “spatial planning and urbanism policy state and involve the actions promoted by the Public Administration, aiming at providing suit- able organisation and usage of the national territory, with the perspective of enhancing its value, namely within the European area, the end objective being the harmonious and sustainable integrated economic, social and cultural development of the country, the different regions and urban agglomerations”. In this sense, this law defines the spatial planning and urbanism policy framework, as well as the land management instruments which enable it to be realised, and regulates the relations between the different levels of the Public Administration and their relations with the general population, as well as with the representatives of the different economic and social interests.
Planeamento Urbano para a Integração de Imigrantes
Book High Commission for Immigration and Ethnic Minorities, ISBN: 989-8000-09-0, 392 pp., April 2006.
Este estudo, realizado no âmbito do planeamento territorial, regional e urbano, focaliza-se a nível estratégico e baseia-se na sistematização, análise e tratamento de informação proveniente dos recenseamentos populacionais e habitacionais (Instituto Nacional de Estatística, 1991, 2001) segundo duas vertentes: o espaço territorial da Área Metropolitana do Porto (a nível de freguesia e de concelho) e os diferentes grupos populacionais, de acordo com o país de origem (incluindo os portugueses).
Planeamento Urbano para a Integrção de Imigrantes
Technical Report Universidade do Porto, February 2005.
Abstract
...
Cálculo Recursivo dos Aproximantes de Frobenius-Padé: Teoria, Estabilidade e Condicionamento
Thesis MSc Thesis, Universidade do Porto, 2004
Abstract
An optimal control problem with state constraints based on a SEIR model to control the spreading of infectious diseases is considered. The main purpose is apply novel theoretical results to successfully validate the numerical solution, computed via direct method. The problem has simple but yet interesting features that we explore in our analysis. Of particular interest is the fact that the state constraint is of order one and that the solution is normal.
Talks
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Airborne Wind Energy Farms: Layout Optimization combining NSGA-II and BRKGA
Conference Talk DIS’24 – 7th International Conference on the Dynamics of Information Systems, Kalamata, Greece, June 2024.
Bibliometric Analysis of Emergent Airborne Wind Energy Systems
Conference Talk ECRES’24 – 12th European Conference on Renewable Energy Systems, Mallorca, Spain, May 2024.
Layout Optimization of Airborne Wind Energy Farms Considering Scaling Effects
Conference Talk ECRES’24 – 12th European Conference on Renewable Energy Systems, Mallorca, Spain, May 2024.
A Multi-Objective Metaheuristic Applied to the Airborne Wind Energy Farm Layout Problem
Conference Talk OLA’24 – 10th Airborne Wind Energy Conference, Madrid, Spain, May 2024.
Airborne Wind Energy Farm: Power Smoothing Strategy
Conference Talk ICACER’24 – 9th International Conference on Advances on Clean Energy Research, Lille, France, April 2024.
Power Smoothing of an Airborne Wind Energy Farm
Conference Talk ICEEER’24 – 8th International Conference on Energy Economics and Energy Policy, Lille, France, April 2024.
Bibliometric Analysis of Airborne Wind Energy for the last decade
Conference Talk AWEC’24 – 10th Airborne Wind Energy Conference, Madrid, Spain, April 2024.
Simplified Path Definition and Path Planning of a Supervisory Controller for Airborne Wind Energy Systems
Conference Talk AWEC’24 – 10th Airborne Wind Energy Conference, Madrid, Spain, April 2024.
Multi–Objective Layout Optimization for Airborne Wind Energy Farms
Conference Talk AWEC’24 – 10th Airborne Wind Energy Conference, Madrid, Spain, April 2024.
Energy Storage System Sizing within a Power Smoothing Strategy for Airborne Wind Energy Farms
Conference Poster AWEC’24 – 10th Airborne Wind Energy Conference, Madrid, Spain, April 2024.
A Biased Random Key Genetic Algorithm to Approach the Kite Wind Energy Farms Layout Problem
Conference Talk Optimization 2023, Aveiro, Portugal, July 2023
Characterisation of the Switching Between Stages in an Airborne Wind Energy System using Optimal Hybrid Control
Conference Talk WESC'23 - Wind Energy Science Conference 2023 | Mini Symposia: Airborne Wind Energy, Glasgow, UK, May 2023
Optimal Layout in Airborne Wind Energy Farms
Conference Talk WESC'23 - Wind Energy Science Conference 2023 | Mini Symposia: Airborne Wind Energy, Glasgow, UK, May 2023
Circular Take–off and Landing for Motorised Kites in Airborne Wind Energy Systems
Conference Talk WESC'23 - Wind Energy Science Conference 2023 | Mini Symposia: Airborne Wind Energy, Glasgow, UK, May 2023
A Combined Path–Following and Model Predictive Control Scheme for kite trajectory control in Airborne Wind Energy Systems
Conference Talk WESC'23 - Wind Energy Science Conference 2023 | Mini Symposia: Airborne Wind Energy, Glasgow, UK, May 2023
Emergency Landing using Deep–stall for Airborne Wind Energy System with Fixed–Wing Kites
Conference Talk WESC'23 - Wind Energy Science Conference 2023 | Mini Symposia: Airborne Wind Energy, Glasgow, UK, May 2023
A Model Predictive Control Scheme to Improve Performance and Enlarge the Domain of Attraction of a Path–following Controller
Conference Talk VC'22 -- 5th Viennese Conference on Optimal Control and Dynamic Games, Wien, Austria, July 2022
Model Predictive Path–Following Control of Airborne Wind Energy Systems with Guaranteed Stability
Conference Talk AWEC'21 - 9th Airborne Wind Energy Conference, Milano, Italy, June 2022
Kite Path–following with L0 and L1 Controllers Tested on a Small–scale Prototype
Conference Talk AWEC'21 - 9th Airborne Wind Energy Conference, Milano, Italy, June 2022
Airborne Wind Energy Farm Layout and Optimization
Conference Poster AWEC'21 - 9th International Airborne Wind Energy Conference, Milano, Italy, June 2022
Optimal switching a formation of Dubins cars
Conference Talk FGP'22 - French German Portuguese 2022 Conference on Optimization, Porto, Portugal, June 2022
Shortest Paths for the Optimal Reorganization of a Nonholonomic Multi–Vehicle Formation
Conference Talk CVIM'21 - The Cape Verde International Days on Mathematics 2021, Praia, Cape Verde, September 2021
Model Predictive Control Scheme to Improve Performance of a Guidance Logic Controller for Trajectory Tracking
Conference Talk EPCO’21 – 8th Portuguese Meeting on Optimal Control (online), June 2021
Comparison of L0 and L1 path-following controllers for Airborne Wind Energy Systems
Conference Talk DCE’21 - 4th Doctoral Congress in Engineering (online), June 2021
Path-Following Model Predictive Control Scheme for Airborne Wind Energy Systems
Conference Talk DCE’21 - 4th Doctoral Congress in Engineering (online), June 2021
Airborne Wind Energy: UPWIND Project
Conference Talk EAWE'20 - European Academy of Wind Energy – 16th EAWE PhD Seminar (online) December 2020
A Model Predictive Control Scheme to Improve Per- formance of a Path-Following Controller for Airborne Wind Energy
Conference Talk IFAC-V 2020 – 1st Virtual IFAC World Congress (online), Berlin, Germany, July 2020.
Optimal Path and Path-Following Control of a Pumping Kite Generator
Conference Poster AWEC’19 – International Airborne Wind Energy Conference, Glasgow, United Kingdom, October 2019
Numerical Computation of Optimal Path and Path- Following Control in Airborne Wind Energy Systems
Conference Talk EUROGEN 2019 - Recent Advances in Numerical Optimization and Optimal Control and its Applications, Guimarães, Portugal, September 2019
Setting the optimal kite location of a kite wind farm for optimal power production
Conference Talk ICEER 2019 – 6th International Conference On Energy and Environment Research, Aveiro, Portugal, July 2019
A Path–following Guidance Method for Airborne Wind Energy Systems with Large Domain of Attraction
Conference Talk ACC’19 – 2019 American Control Conference, Philadelphia, USA, July 2019
Shortest Paths for the Optimal Reorganiza- tion of a Nonholonomic Multi–Vehicle Formation
Conference Talk VI Workshop on Computational Data Analysis and Numerical Methods, Covinhã, Portugal, 28-30 June 2019
Optimal Path and Optimal Path–Following of Airborne Wind Energy Systems
Conference Poster EPCO’19 – 7th Portuguese Meeting on Optimal Control, Porto, Portugal, 25 June 2019
Euler–Pseudospectral method and a wavelet–based mesh generation strategy for the adaptive solution of optimal control problems
Conference Poster EPCO’19 – 7th Portuguese Meeting on Optimal Control, Porto, Portugal, 25 June 2019
Solvers and Interfaces for Optimal Control: an updated overview
Talk Faculdade de Engenharia, U. Porto, Porto, 27th May 2019
A hp–h Adaptive Time–mesh Refinement Al- gorithm for Solving Optimal Control Problems
Conference Talk SYMCOMP’19 - 4th International Conference on Numerical and Symbolic Computation Developments and Applications, Porto, Portugal, April 2019
Guaranteed Constraint Satisfaction in Continuous–Time Control Problems
Conference Talk CDC’18 – 57th IEEE Conference on Decision and Control, Miami Beach, Florida, USA, December 2018
AMR-MPC: Sampled–data Model Predictive Control Using Adaptive Time– mesh Refinement, with Stability Guarantees
Conference Poster NMPC’18 Proceedings – 6th IFAC Conference on Nonlinear Model Predictive Control, Madison, Wisconsin, USA, August 2018
A Trajectory Controller for Kite Power Systems with Wind Gust Handling Capabilities
Conference Talk ICINCO’18 – 15th International Conference on Informatics in Control, Automation and Robotics, Porto, Portugal, July 2018
On the problem of kite location in airborne wind energy farms
Conference Talk EURO’18 – 29th European Conference on Operation Research, Valencia, Spain, July 2018
Stability Conditions for Sampled–data Model Predictive Control with Adap- tive Time–mesh Refinement
Conference Talk EPCO’18 – 6th Portuguese Meeting on Optimal Control, Coimbra, Portugal, June 2018
Optimal Reorganization of a Formation of Nonholonomic Agents Using Shortest Paths
Conference Talk CONTROLO’18 – 13th APCA International Conference on Control and Soft Computing, Ponta Delgada, Azores, Portugal, June 2018
Guaranteed Collision Avoidance in Multi–Kite Power Systems
Conference Talk AWEC’17 – International Airborne Wind Energy Conference, Freiburg, Germany, October 2017
An Adaptive Mesh Refinement Algorithm with Time–dependent Criteria for Model Predictive Control
Conference Talk Optimization 2017, Lisboa, 6-8 September 2017
Optimal Control of Kite Power Systems: Mesh-Refinement Strategies
Conference Talk ICEER’17 – 4th International Conference On Energy and Environment Research, Porto, 17-20 July 2017
Optimal Control of Underwater Kite Power Systems
Conference Talk ICEA’17 – 2017 International Conference in Engineering Applications - Energy and Sustainability in Small Developing Economies, Funchal, 10-12 July 2017
A Time-dependent Adaptive Mesh Refinement Scheme for Model Predictive Control
Conference Poster NHOC’17 – New Horizons in Optimal Control: A tribute to Helmut Maurer, Urszula Ledzewicz and Heinz Schaettler, Porto, 3-5 July 2017
Trajectories with Guaranteed Constraint Satisfaction in Numerically-solved Continuous-Time Optimal Control Problems
Conference Talk EPCO’17 – 5th Portuguese Meeting on Optimal Control, Lisboa, 12th June 2017
Electricity Generation via Optimal Control of Underwater Kite Power Systems
Conference Poster EPCO’17 – 5th Portuguese Meeting on Optimal Control, Lisboa, 12th June 2017
Efficient Algorithms for Optimization-based Control
Invited Talk LEMA Seminar, Instituto Superior de Engenharia do Porto, Porto, 5th April 2017
Sampled-data Model Predictive Control using Adaptive Time-Mesh Refinement Algorithms
Conference Talk CONTROLO’16 - 12th Portuguese Conference on Automatic Control, Guimarães, Portugal, 14-16 September 2016
Optimal Control of Constrained Nonlinear Systems: An adaptive time-grid refinement algorithm guided by the adjoint multipliers
Conference Talk ICCOPT’16 - 5th International Conference on Continuous Optimization, Tokyo, Japão, 6-11 August 2016
Adapting a Time-Mesh to each Optimal Control Problem
Conference Talk ENSPM’16 - Encontro Nacional da Sociedade Portuguesa de Matemática, Barreiro, Portugal, July 2016
Optimization-based Control of Nonlinear Systems using Adaptive Time-grid Refinement Algorithms
Conference Talk RTDE’16 - Recent Trends in Difierential Equations, Aveiro, Portugal, June 2016
Optimal Control of Constrained Nonholonomic Systems: Adaptive Time-grid Refinement Algorithms
Conference Talk NUMTA’16 - 2nd International Conference and Summer School - Numerical Computations: Theory and Algorithms, Calabria, Italy, June 2016
An Adaptive Mesh Refinement Algorithm for Model Predictive Control
Conference Talk EPCO’16 – 4th Portuguese Meeting on Optimal Control, Porto, Portugal, June 2016
An Adaptive Mesh Refinement Method for State Constrained Optimal Control Problems
Conference Talk EPCO’15 – 3rd Portuguese Meeting on Optimal Control, Guimarães, Portugal, September 2015
Optimal Control and Model Predictive Control of Kite Power Systems
Conference Talk EPCO’15 – 3rd Portuguese Meeting on Optimal Control, Guimarães, Portugal, September 2015
NMB Target Level Tracking based on an Optimal Control Problem
Conference Talk EPCO’15 – 3rd Portuguese Meeting on Optimal Control, Guimarães, Portugal, September 2015
An Adaptive Mesh Refinement Algorithm for Optimal Control Problems
Conference Talk SIAM'15 - Conference on Control and Its Applications, Paris, France, July 2015
Reference Tracking of Depth of Anesthesia Using Optimal Control
Conference Talk SIAM'15 - Conference on Control and Its Applications, Paris, France, July 2015
An Optimal Control Approach to Reference Level Tracking in General Anesthesia
Conference Talk MED'15 - 23rd Mediterranean Conference on Control and Automation, Torremolinos, Spain, 16-19 June 2014
Mesh-Refinement Strategies for Fast Optimal Control and Model Predictive Control of Kite Power Systems
Conference Poster AWEC’15 - Airborne Wind Energy Conference, Delft, The Netherlands, 15-16 June 2015
Numerical Methods for Optimal Control and Model Predictuve Control
Talk Faculdade de Ciências, U. Porto, Porto, 19th December 2014
A Multi-Level Time-Grid Refinement Algorithm to Solve Optimal Control Problems
Conference Poster NHOC’14 - New Horizons in Optimal Control, Cascais, Portugal, 8-10 September 2014
An Adaptive Time-Mesh Refinement in Optimal Control
Conference Talk Conference on Optimization Control and Applications in the Information Age: 60th birthday of Panos Pardalos, Chalkidiki, Greece, June 2014
Multi-Level Adaptive Time-Mesh Refinement in Optimal Control Problems
Conference Talk EPCO’14 – 2nd Portuguese Meeting on Optimal Control, Aveiro, Portugal, June 2014
Mesh Refinement in Optimal Control: Nonholonomic Vehicles Maneuver Problems
Conference Talk DAOC'14 – Industrial Workshop on Safety Systems, Driver Assistance and Optimal Control, organized by Volkswagen A.G., Wolfsburg, Germany, January 2014
Time-Mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles
Conference Talk CETC'13 - Conference on Electronics, Telecommunications and Computers, Lisboa, Portugal, 5-6 December 2013
Introducing State Constraints in Optimal Control in Health Problems
Conference Poster CETC'13 - Conference on Electronics, Telecommunications and Computers, Lisboa, Portugal, 5-6 December 2013
Mesh Refinement Strategy for Optimal Control Problems
Conference Talk ICNAAM'13 – 11th International Conference in Numerical Analysis and Applied Mathematics, Rhodes, Greece, September 2013
Health Problems with Constraints
Conference Talk Health Problems with Constraints, OMPC'13 – Summer school and workshop on optimal and model predictive control, Bayreuth, Germany, September 2013
Optimal Control of a SEIR Epidemic Model with Mixed and State Constraints
Conference Talk 16th French-German-Polish Conference on Optimization, Cracóvia, Poland, September 2013
Time-Grid Refinement Strategy in Optimal Control Problems
Talk Faculdade de Engenharia, U. Porto, Porto, 9th July 2013
Overcoming Obstacles in Optimal Control
Invited Talk Controlo Óptimo Fora de Horas, Instituto Superior de Engenharia do Porto, Porto, 19th June 2013
Optimal Control Problems: Software and Time Grid Strategy
Talk Faculdade de Engenharia, U. Porto, Porto, 29th April 2013
Optimal Control Problems: Solvers and Interfaces
Conference Talk EPCO’13 – 1st Portuguese Meeting on Optimal Control, Porto, Portugal, February 2013
Optimal Control Applied to Infectious Diseases: SEIR Epidemic Model
Conference Talk EPCO’13 – 1st Portuguese Meeting on Optimal Control, Porto, Portugal, February 2013
Recent developments on AMR: 2D Advection equation
Talk Faculdade de Engenharia, U. Porto, Porto, 13th October 2011
Cuxac Cabardes: a canopy model benchmark
Talk Faculdade de Engenharia, U. Porto, Porto, 29th June 2011
AMR with PARAMESH: enforcing flux conservation
Talk Faculdade de Engenharia, U. Porto, Porto, 6th April 2011
The representativeness of microscale CFD results: Characterization of wind conditions over complex terrain
Conference Talk EERA'11 – European Energy Research Alliance - Workshop on Wind Conditions, Porto, Portugal, January 2011
AMR with PARAMESH: code implementation
Talk Faculdade de Engenharia, U. Porto, Porto, 16th December 2010
Adaptive mesh refinement: 2D Poisson’s equation
Talk Faculdade de Engenharia, U. Porto, Porto, 29th September 2010
Modelling a wind power curve
Talk Faculdade de Ciências, U. Porto, Porto, 12th June 2010
Adaptive mesh refinement: first impressions
Talk Faculdade de Engenharia, U. Porto, Porto, 11th June 2010
Analysis of the similarity in turbulence intensity and wind shear as function of the wind velocity: Field measurements and numerical results
Conference Talk EWEC'10 – European Wind Energy Conference, Poland, April 2010
Modelação da curva de potência no âmbito da previsão da produção de energia eléctrica de base eólica
Conference Talk I Semana do Ambiente, Porto, Portugal, February 2010
Determining a wind turbine power curve from real data
Talk Faculdade de Engenharia, U. Porto, Porto, 19th January 2010
Adaptive mesh refinement in computational fluid dynamics of turbulent flows
Talk Faculdade de Ciências, U. Porto, Porto, 19th December 2009
A more accurate procedure for modelling a wind turbine power curve
Conference Poster 1st Porto Meeting of Mathematicians for Industry, Porto, Portugal, 17-18 April 2009
EPREV2 – Cálculo da Matriz de Potência utilizando modelos não-lineares: Parque Lagoa D.João e Parque do Passarinho
Talk Faculdade de Engenharia, U. Porto, Porto, 23th Mars 2009
Modelling the slip potential fault activity in the Horseshoe Abyssal Plain (Gulf of Cadiz): implications for seismic hazard
Conference Poster EGU'08 - European Geosciences Union General Assembly, Vienna, Austria, 13-18 April 2008
A New Graphical Software Tool To Analyze The Slip Potential Of Faults
Conference Poster 6th Portuguese and Spanish Assembly of Geodesy and Geophysics, Tomar, Portugal, 11-14 February 2008
Aproximação Racional de Séries de Polinómios Ortogonais
Invited Talk Seminários de Matemática, Instituto Superior de Engenharia do Porto, Porto, 1st February 2006
Orthogonal Polinomials – A New Add-on
Conference Talk Wolfram Technology Conference, Champaign, Illinois, USA, October 2005
Estabilidade e Condicionamento do Cálculo Recursivo dos Aproximantes de Frobenius-Padé
Invited Talk Seminário Diagonal, Dept. de Matemática Aplicada, Faculdade de Ciências da U. Porto, Porto, 27th April 2005
Estabilidade numérica do cálculo recursivo dos Aproximantes de Frobenius-Padé: utilização CADNA
Talk Faculdade de Engenharia, U. Porto, Porto, 30th June 2003
Conferences
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Scientific CommitteCONTROLO 2020 – 14th International Conference on Automatic Control and Soft ComputingPolithecnic Institute of Bragança, Bragança, Portugal, July 1st–3rd 2020EPCO'19 – 7th Portuguese Meeting on Optimal ControlFaculty of Engineering, U.Porto, Porto, Portugal, June 25th 2019
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Organizing CommitteeEPCO'19 – 7th Portuguese Meeting on Optimal ControlFaculty of Engineering, U.Porto, Porto, Portugal, June 25th 2019EPCO'16 – 4th Portuguese Meeting on Optimal ControlSchool of Engineering, P.Porto, Porto, Portugal, June 20th 2016.EPCO'15 – 3th Portuguese Meeting on Optimal ControlSciences School, U.Minho, Guimarães, Portugal, September 15th 2015StudECE'13 – 2nd PhD Students Conference in Electrical and Computer EngineeringSchool of Engineering, P.Porto, Porto, Portugal, June 26th 2013
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Other Events1st MAP–PDMA Students WorkshopMembro da Mesa Redonda: ”Aspetos Cruciais na Empregabilidade de Doutorados em Matemática na Industria”, Universidade do Minho, Braga, Portugal, 29-30 June 2017
Education
Academic Education
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2014 Ph.D.
Applied Mathematics
University of Porto, Faculty of Sciences, Porto
Numerical Methods for Optimal Control and Model Predictive Control
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2004 M.Sc.
Computer Methods for Sciences & Engineering
University of Porto, Faculty of Sciences, Porto
Frobenius-Padé Approximants: Theory, Stability and Conditioning
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2002 First degree
Applied Mathematics
University of Porto, Faculty of Sciences, Porto
Specialisations
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2014
Global Optimization: Models, Algorithms, Software and Applications
University of Aveiro, 12h, Aveiro
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2005
Authoring in Mathematica
Wolfram Research, 5h, Illinois, USA
Entrepreneurship Courses
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2016 COHiTEC
COHiTEC Program
Turning Science into BusinessCOTEC, Porto Business School
100h, Porto
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2007 JEEP
Jovens Empresários de Elevado Potencial
Associação para o Desenvolvimento de Estudos Aplicados em Ciências Empresariais
400h, Porto
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2004 PAECE
Programa Avançado em Empreendedorismo, Criação de Empresas e Desenvolvimento de Negócios
Associação Nacional de Jovens Empresários
200h, Porto
Other Courses
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2005
Elaboração do Plano de Formação
Associação Nacional de Jovens Empresários
36h, Porto
Contact & Meet Me
I would be glad to talk to you if you need my assistance in your research.
- lab: +351-22 508 1450
- ltpaiva@fe.up.pt
- Authenticus
At My Lab
You can find me at the Lab. I202.