Recent Academic Positions

  • 2017 Present

    FCT Postdoctoral Fellow

    DEEC, Faculty of Engineering, University of Porto, Porto

  • 2017

    Invited Lecturer

    DMA, School of Engineering, Polytechnic of Porto, Porto

  • 2015 2017

    Postdoctoral Research Associate

    DEEC, Faculty of Engineering, University of Porto, Porto

Academic Education

  • 2014 Ph.D.

    Applied Mathematics

    University of Porto, Faculty of Science, Porto

  • 2004 M.Sc.

    Computer Methods for Sciences & Engineering

    University of Porto, Faculty of Science, Porto

  • 2002 First degree

    Applied Mathematics

    University of Porto, Faculty of Science, Porto

Awards, Honors and Grants

  • July 2017
    Best Paper Award
    Optimal Control of Underwater Kite Power Systems
    Luís Tiago Paiva, F.A.C.C. Fontes
    International Conference in Engineering Applications, Funchal, 10-12 July 2017
  • March 2017
    FCT Post-doctoral Fellowship
    Global Optimisation-based Control of Hybrid Systems
    Ref.: SFRH/BPD/126683/2016
    Faculty of Engineering, University of Porto, Porto, Portugal

Supervision

  • 2013-2014
    Optimal Control of Power Kites for Wind Power Production
    Supervisor Luis Tiago Paiva
    Tiago Costa Moreira Maia
    Master in Electrical and Computers Engineering (co‐supervisor)
    University of Porto, Faculty of Engineering, Porto

Teaching History

Invited Lecturer

Department of Mathematics, School of Engineering, Polytechnic of Porto, Porto

  • 2017 2016

    Mathematics 1

    First degree in Automotive Engineering

Assistant Lecturer

Faculty of Science and Technology, University Fernando Pessoa, Porto

  • 2012 2011

    Numerical Analysis

    First degree in Civil Engineering, Computer Engineering, Environmental Engineering, Engineering and Quality Management

  • 2011 2010

    Numerical Analysis¹ & Foundations of Mathematics²

    ¹First degree in Civil Engineering, Computer Engineering, Environmental Engineering, Engineering and Quality Management
    ²First degree in Business Sciences

  • 2010 2009

    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

  • 2009 2008

    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

  • 2006 2005

    Calculus

    First degree in Physics

  • 2005 2004

    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

  • 2004 2003

    Numerical Analysis 2¹ & Calculus²

    ¹First degree in Applied Mathematics and Mathematics Applied to Technology
    ²First degree in Physics

Research Projects

  • 2017-Today
    Global Optimisation-based Control of Hybrid Systems
    Global Optimisation-based Control of Hybrid Systems
    Ref.: SFRH/BPD/126683/2016 (FCT Post-doctoral Grant)
    University of Porto, Faculty of Engineering, Porto
  • 2016-Today
    Theory, Applications and Numerics of Optimal Control
    TOCCATA - Teoria, Aplicações e Computação Numérica de Controlo Ótimo
    Ref.: PTDC/EEI‐AUT/2933/2014
    University of Porto, Faculty of Engineering, Porto
  • 2015
    Optimal Control: Health, Energy and Robotics Applications
    OCHERA - Controlo Óptimo: Aplicações em Saúde, Energia e Robótica
    Ref.: PTDC/EEI-AUT/1450/2012
    University of Porto, Faculty of Engineering, Porto
  • 2015
    Smart Manufacturing and Logistics
    Produção e Logística Inteligentes
    Ref.: NORTE-07-0124-FEDER-000057
    INESC-TEC, Porto
  • 2014
    Smart Forecast Systems for Energy and Water Management
    SMART4CAST - Sistemas Inteligentes de Previsão para Gestão de Energia e Água
    Ref.: FEUP/SMARTWATT/2014
    University of Porto, Faculty of Engineering, Porto
  • 2014
    Optimal Control: Health, Energy and Robotics Applications
    OCHERA - Controlo Óptimo: Aplicações em Saúde, Energia e Robótica
    Ref.: PTDC/EEI-AUT/1450/2012
    University of Porto, Faculty of Engineering, Porto
  • 2012-2013
    Optimal Control for Constrained, Nonlinear & Hybrid Systems
    OCCOHyNS - Controlo Óptimo em Sistemas Não Lineares Híbridos e com Restrições
    Ref.: PTDC/EEA-CRO/116014/2009
    University of Porto, Faculty of Engineering, Porto
  • 2009-2011
    High Performance Computing of Wind Over Complex Terrain
    COMPWIND - Computação de elevado desempenho do vento sobre terreno complexo
    Ref.: PTDC/ENR/71216/2006
    University of Porto, Faculty of Engineering, Porto
  • 2007-2008
    Seismic Risk and Tsunamis in the Algarve
    ERSTA - Estudo do risco sismico e de tsunamis do Algarve
    Ref.: IME/AUR/49901/2003
    University of Porto, Faculty of Engineering, Porto
  • 2004-2005
    Urban Planning for Immigrant Integration
    Planeamento Urbano para a Integração de Imigrantes
    Ref.: IME/AUR/49901/2003
    University of Porto, Faculty of Engineering, Porto

Research Work

  • FCT Postdoctoral Follow in Global Optimisation at FEUP
    August|2017 - Present

    Global Optimisation-based Control of Hybrid Systems

    FCT Postdoctoral Follow at the Department of Electrical and Computer Engineering

  • Postdoctoral Research Associate in AWEC at FEUP
    July|2015 - July|2017

    Adaptive Mesh Refinement Schemes for Optimal Control and Model Predictive Control

    Postdoctoral Research Associate at the Department of Electrical and Computer Engineering

  • Postdoctoral Research Associate in Manufacturing and Logistics at INESC
    March|2015 - June|2015

    Smart Manufacturing and Logistics

    Postdoctoral Research Associate at the Laboratory of Artificial Intelligence and Decision Support

  • Research Assistant in Optimal Control at FEUP
    March|2012 - March|2015

    Optimal control for constrained, nonlinear and hybrid systems

    Research Assistant at the Department of Electrical and Computer Engineering

    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.

  • PhD Candidate in Wind Energy at CESA
    October|2008 - February|2012

    Adaptive mesh refinement in computational fluid dynamics of turbulent flows

    Research Assistant at the Department of Mechanical Engineering

    Main responsibilities: To develop algorithms for adaptive mesh refinement to be added to a CFD code developed in the Research Centre for Wind Energy and Atmospheric Flows.

    Software: Matlab, OpenFOAM, PARAMESH, Tecplot, VENTOS.

  • Research Assistant in Geophysics at Universidade do Algarve
    September|2007 - August|2008

    Seismic Risk and Tsunamis in the Algarve

    Research Assistant at the Department of Geophysics

    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.

  • image
    February|2006 - August|2007

    WeMapp - Opportunity Search Engine

    Researcher at Competinov

    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.

  • image
    February|2005 - January|2006

    Automatic Construction of Orthogonal Polynomials and Their Characterizations

    Research Assistant at the Centre for Mathematics of the University of Porto

    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.

  • Research Assistant in Neural Networks at FEUP
    February|2004 - January|2005

    Urban Planning for Immigrants Integration

    Research Assistant at the Department of Civil Engineering

    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.

Filter by type:

Sort by year:

Optimal control of kite power systems: mesh–refinement strategies

Luís Tiago Paiva, F.A.C.C. Fontes
Journal 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

Luís Tiago Paiva, F.A.C.C. Fontes
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

F.A.C.C. Fontes, Luís Tiago Paiva
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

Luís Tiago Paiva, F.A.C.C. Fontes
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

J. Almeida, Luís Tiago Paiva, T. Mendonça, P. Rocha
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

J. Almeida, Luís Tiago Paiva, T. Mendonça, P. Rocha
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

Luís Tiago Paiva, F.A.C.C. Fontes
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

Luís Tiago Paiva
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

Luís Tiago Paiva, F.A.C.C. Fontes
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

I. Kornienko, Luís Tiago Paiva, M.d.R. de Pinho
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

Luís Tiago Paiva, C. Veiga Rodrigues, J.M.L.M. Palma
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

M.H.A. Biswas, Luís Tiago Paiva, M.d.R. Pinho
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

Luís Tiago Paiva, F.A.C.C. Fontes
Conference Paper in AIP Conference Proceedings, 1558 (1), pp. 590-593, October 2013 | doi: 10.1063/1.4825560

Abstract

...

Optimal Control for Constrained Hybrid System: Computational Libraries and Applications

Luís Tiago Paiva
Technical Report Universidade do Porto, February 2013.

Abstract

...

Analysis of the Similarity in Turbulence Intensity and Wind Shear as Function of the Wind Velocity: Field Measurements and Numerical Results

C. Veiga Rodrigues, J. Matos, Luís Tiago Paiva, J.M.L.M. Palma
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

M.C. Neves, Luís Tiago Paiva, J. Luís
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

Luís Tiago Paiva, M.C. Neves, J. Luís
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

E.M. Rebelo, Luís Tiago Paiva
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

E.M. Rebelo, Luís Tiago Paiva
Book High Commission for Immigration and Ethnic Minorities, ISBN: 989-8000-09-0, 392 pp., April 2006.
image

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

E.M. Rebelo, Luís Tiago Paiva
Technical Report Universidade do Porto, February 2005.

Abstract

...

Cálculo Recursivo dos Aproximantes de Frobenius-Padé: Teoria, Estabilidade e Condicionamento

Luís Tiago Paiva
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.

Filter by type:

Sort by year:

An Adaptive Mesh Refinement Algorithm with Time–dependent Criteria for Model Predictive Control

Luís Tiago Paiva, F.A.C.C. Fontes
Conference Talk Optimization 2017, Lisboa, 6-8 September 2017

Optimal Control of Kite Power Systems: Mesh-Refinement Strategies

Luís Tiago Paiva, F.A.C.C. Fontes
Conference Talk ICEER’17 – 4th International Conference On Energy and Environment Research, Porto, 17-20 July 2017

Optimal Control of Underwater Kite Power Systems

Luís Tiago Paiva, F.A.C.C. Fontes
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

Luís Tiago Paiva, F.A.C.C. Fontes
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

F.A.C.C. Fontes, Luís Tiago Paiva
Conference Talk EPCO’17 – 5th Portuguese Meeting on Optimal Control, Lisboa, 12th June 2017

Electricity Generation via Optimal Control of Underwater Kite Power Systems

Luís Tiago Paiva, F.A.C.C. Fontes
Conference Poster EPCO’17 – 5th Portuguese Meeting on Optimal Control, Lisboa, 12th June 2017

Efficient Algorithms for Optimization-based Control

Luís Tiago Paiva, F.A.C.C. Fontes
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

Luís Tiago Paiva, F.A.C.C. Fontes
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

F.A.C.C. Fontes, Luís Tiago Paiva
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

Luís Tiago Paiva, F.A.C.C. Fontes
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

Luís Tiago Paiva, F.A.C.C. Fontes
Conference Talk RTDE’16 - Recent Trends in Difierential Equations, Aveiro, Portugal, June 2016

Optimal Control of Constrained Nonholonomic Systems: Adaptive Time-grid Refinement Algorithms

F.A.C.C. Fontes, Luís Tiago Paiva
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

Luís Tiago Paiva, F.A.C.C. Fontes
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

Luís Tiago Paiva, F.A.C.C. Fontes
Conference Talk EPCO’15 – 3rd Portuguese Meeting on Optimal Control, Guimarães, Portugal, September 2015

Optimal Control and Model Predictive Control of Kite Power Systems

F.A.C.C. Fontes, Luís Tiago Paiva
Conference Talk EPCO’15 – 3rd Portuguese Meeting on Optimal Control, Guimarães, Portugal, September 2015

NMB Target Level Tracking based on an Optimal Control Problem

J. Almeida, Luís Tiago Paiva, T. Mendonça, P. Rocha
Conference Talk EPCO’15 – 3rd Portuguese Meeting on Optimal Control, Guimarães, Portugal, September 2015

An Adaptive Mesh Refinement Algorithm for Optimal Control Problems

F.A.C.C. Fontes, Luís Tiago Paiva
Conference Talk SIAM'15 - Conference on Control and Its Applications, Paris, France, July 2015

Reference Tracking of Depth of Anesthesia Using Optimal Control

J. Almeida, Luís Tiago Paiva, T. Mendonça, P. Rocha
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

J. Almeida, Luís Tiago Paiva, T. Mendonça, P. Rocha
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

Luís Tiago Paiva, F.A.C.C. Fontes
Conference Poster AWEC’15 - Airborne Wind Energy Conference, Delft, The Netherlands, 15-16 June 2015

Numerical Methods for Optimal Control and Model Predictuve Control

Luís Tiago Paiva
Talk Faculdade de Ciências, U. Porto, Porto, 19th December 2014

A Multi-Level Time-Grid Refinement Algorithm to Solve Optimal Control Problems

Luís Tiago Paiva, F.A.C.C. Fontes
Conference Poster NHOC’14 - New Horizons in Optimal Control, Cascais, Portugal, 8-10 September 2014

An Adaptive Time-Mesh Refinement in Optimal Control

F.A.C.C. Fontes, Luís Tiago Paiva
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

Luís Tiago Paiva, F.A.C.C. Fontes
Conference Talk EPCO’14 – 2nd Portuguese Meeting on Optimal Control, Aveiro, Portugal, June 2014

Mesh Refinement in Optimal Control: Nonholonomic Vehicles Maneuver Problems

Luís Tiago Paiva, F.A.C.C. Fontes
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

Luís Tiago Paiva, F.A.C.C. Fontes
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

Igor Kornienko, Luís Tiago Paiva, M.d.R. de Pinho
Conference Poster CETC'13 - Conference on Electronics, Telecommunications and Computers, Lisboa, Portugal, 5-6 December 2013

Mesh Refinement Strategy for Optimal Control Problems

Luís Tiago Paiva, F.A.C.C. Fontes
Conference Talk ICNAAM'13 – 11th International Conference in Numerical Analysis and Applied Mathematics, Rhodes, Greece, September 2013

Health Problems with Constraints

Igor Kornienko, Luís Tiago Paiva, M.H.A. Biswas, M.d.R. de Pinho
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

M.d.R. de Pinho, M.H.A. Biswas, Igor Kornienko, Luís Tiago Paiva
Conference Talk 16th French-German-Polish Conference on Optimization, Cracóvia, Poland, September 2013

Time-Grid Refinement Strategy in Optimal Control Problems

Luís Tiago Paiva
Talk Faculdade de Engenharia, U. Porto, Porto, 9th July 2013

Overcoming Obstacles in Optimal Control

Luís Tiago Paiva
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

Luís Tiago Paiva
Talk Faculdade de Engenharia, U. Porto, Porto, 29th April 2013

Optimal Control Problems: Solvers and Interfaces

Luís Tiago Paiva
Conference Talk EPCO’13 – 1st Portuguese Meeting on Optimal Control, Porto, Portugal, February 2013

Optimal Control Applied to Infectious Diseases: SEIR Epidemic Model

M.H.A. Biswas, Luís Tiago Paiva, M.d.R. de Pinho
Conference Talk EPCO’13 – 1st Portuguese Meeting on Optimal Control, Porto, Portugal, February 2013

Recent developments on AMR: 2D Advection equation

Luís Tiago Paiva
Talk Faculdade de Engenharia, U. Porto, Porto, 13th October 2011

Cuxac Cabardes: a canopy model benchmark

Luís Tiago Paiva
Talk Faculdade de Engenharia, U. Porto, Porto, 29th June 2011

AMR with PARAMESH: enforcing flux conservation

Luís Tiago Paiva
Talk Faculdade de Engenharia, U. Porto, Porto, 6th April 2011

The representativeness of microscale CFD results: Characterization of wind conditions over complex terrain

J.M.L.M. Palma, C. Veiga Rodrigues, Luís Tiago Paiva
Conference Talk EERA'11 – European Energy Research Alliance - Workshop on Wind Conditions, Porto, Portugal, January 2011

AMR with PARAMESH: code implementation

Luís Tiago Paiva
Talk Faculdade de Engenharia, U. Porto, Porto, 16th December 2010

Adaptive mesh refinement: 2D Poisson’s equation

Luís Tiago Paiva
Talk Faculdade de Engenharia, U. Porto, Porto, 29th September 2010

Modelling a wind power curve

Luís Tiago Paiva
Talk Faculdade de Ciências, U. Porto, Porto, 12th June 2010

Adaptive mesh refinement: first impressions

Luís Tiago Paiva
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

C. Veiga Rodrigues, J. Matos, Luís Tiago Paiva, J.M.L.M. Palma
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

Luís Tiago Paiva, C. Veiga Rodrigues, J.M.L.M. Palma
Conference Talk I Semana do Ambiente, Porto, Portugal, February 2010

Determining a wind turbine power curve from real data

Luís Tiago Paiva
Talk Faculdade de Engenharia, U. Porto, Porto, 19th January 2010

Adaptive mesh refinement in computational fluid dynamics of turbulent flows

Luís Tiago Paiva
Talk Faculdade de Ciências, U. Porto, Porto, 19th December 2009

A more accurate procedure for modelling a wind turbine power curve

Luís Tiago Paiva, C. Veiga Rodrigues, J.M.L.M. Palma
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

Luís Tiago Paiva
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

M.C. Neves, Luís Tiago Paiva, D. Vales
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

Luís Tiago Paiva, M.C. Neves, J. Luís
Conference Poster 6th Portuguese and Spanish Assembly of Geodesy and Geophysics, Tomar, Portugal, 11-14 February 2008

Aproximação Racional de Séries de Polinómios Ortogonais

Luís Tiago Paiva
Invited Talk Seminários de Matemática, Instituto Superior de Engenharia do Porto, Porto, 1st February 2006

Orthogonal Polinomials – A New Add-on

M.C. Neves, Luís Tiago Paiva, J. Luís
Conference Talk Wolfram Technology Conference, Champaign, Illinois, USA, October 2005

Estabilidade e Condicionamento do Cálculo Recursivo dos Aproximantes de Frobenius-Padé

Luís Tiago Paiva
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

Luís Tiago Paiva
Talk Faculdade de Engenharia, U. Porto, Porto, 30th June 2003

Academic Education

  • 2014 Ph.D.

    Applied Mathematics

    University of Porto, Faculty of Sciences, Porto

    Numerical Methods for Optimal Control and Model Predictive Control

  • 2004 M.Sc.

    Computer Methods for Sciences & Engineering

    University of Porto, Faculty of Sciences, Porto

    Frobenius-Padé Approximants: Theory, Stability and Conditioning

  • 2002 First degree

    Applied Mathematics

    University of Porto, Faculty of Sciences, Porto

Specialisations

  • 2014

    Global Optimization: Models, Algorithms, Software and Applications

    University of Aveiro, 12h, Aveiro

  • 2005

    Authoring in Mathematica

    Wolfram Research, 5h, Illinois, USA

Entrepreneurship Courses

  • 2016 COHiTEC

    COHiTEC Program
    Turning Science into Business

    COTEC, Porto Business School

    100h, Porto

  • 2007 JEEP

    Jovens Empresários de Elevado Potencial

    Associação para o Desenvolvimento de Estudos Aplicados em Ciências Empresariais

    400h, Porto

  • 2004 PAECE

    Programa Avançado em Empreendedorismo, Criação de Empresas e Desenvolvimento de Negócios

    Associação Nacional de Jovens Empresários

    200h, Porto

Other Courses

  • 2005

    Elaboração do Plano de Formação

    Associação Nacional de Jovens Empresários

    36h, Porto

At My Lab

You can find me at the Lab. I202.