# Luís Tiago Paiva

12.06

· PhDAbout

25

Research items

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82

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Introduction

**Skills and Expertise**

MATLAB SimulationModeling and SimulationNumerical SimulationNumerical AnalysisEngineering, Applied and Computational MathematicsUrban PlanningAlgorithmsMathematical ModellingMATLABAutomationApplied MathematicsSoftware EngineeringAnalysisPredictionSpatial PlanningControl Systems EngineeringProgramming LanguagesForecastingComputational StatisticsComputationWind EnergyWind EngineeringOptimal ControlWindParameter IdentificationWind TurbinesGridModel Predictive ControlAutomatic ControlOpen Source SoftwareOptimal Control TheoryStatistical Techniques

Research Experience

Aug 2017

- Departamento de Engenharia Eletrotécnica e de Computadores
- Porto, Porto, Portugal

Position

- FCT PostDoc Fellow

Jul 2015 - Jul 2017

Education

Oct 2008 - Dec 2014

Nov 2002 - Apr 2004

Sep 1998 - Sep 2002

Current institution

- Departamento de Engenharia Eletrotécnica e de Computadores
- Porto, Portugal

Current position

- FCT PostDoc Fellow

**Lab head**

Top co-authors

Awards & Achievements (2)

Grant · Aug 2017

Global Optimisation-based Control of Hybrid Systems

Award · Jul 2017

Best Paper - Optimal control of underwater kite power systems

Network

Co-authors

Followers

Following

Projects

Projects (3)

Project

This project aims to contribute to the development of Optimal Control methods and applications. It focuses on building bridges
between theory, applications and numerical treatment of optimal control problems by solving a selected number of problems from
different areas.
This project is launched as a continuation of the work initialized with the FCT project PTDC/EEI-AUT/1450/2012|FCOMP-01-0124-
FEDER-028894. It brings together a renewed researcher team with a multidisciplinary background including Optimal Control Theory,
Control Engineering, Optimization and Numerical Analysis to work on theoretical developments in conjunction with interesting and
relevant applications of optimal control.
We seek to bring together major Portuguese research centers in Optimal Control to promote the exchange of experience and
knowledge based on on-going research activities, the training of young researchers and to deliver value to the society. The
proposed Research Team will collaborate closely with EU and American research groups to explore new research methods and to
promote the introduction of optimal control methods on different areas. We aim to contribute to the creation of a vibrant, productive
and efficient optimal control research community, to attract young researchers, to increase awareness of the benefits of optimal
control areas as different as biomedicine and economics and to deliver value to the society.
While the driving force behind the choice of applications to be studied will be the need to test and illustrate recent theoretical
advances, we expect the applications themselves to trigger new theoretical development. Many results leading to a characterization
of solution to optimal control problems may be used to validate numerical solutions (i.e., to verify that a certain solution is possibly
an optimal solution). However, the numerical verification of optimality is in general a hard task. We hope to remedy some of these
situations by proposing numerically verifiable optimality conditions and such conditions on regularity and normality. Special
attention will be paid to problems with state constraints, mixed constraints, bang-bang controls, singular controls, bang-singular
junctions. We shall also be concerned with the synthesis of controlled trajectories, sensitivity analysis of the solutions to parameters
and Model Predictive Control techniques.
Selected problems from biomedicine, such as epidemiology, power systems; economics and also more classical areas such as the
planning of trajectories of unmanned vehicles will be considered. The challenges related to applied problems that will be addressed
can be divided into four classes
a) formulation of the problems for some applications;
b) solving the problems numerically via optimization methods;
c) establishing the optimality of the numerical solution;
d) connections between the types of solutions and concepts of the application under study.
While b) and c) fall within the expertise of the research team, their collaborators and the project advisory board, items a) and d)
above will be conducted in close consultation with experts on the specific area of the applied problems.
The choice of problems is based primarily on their societal interest but it is done to ascertain that their
analytical treatment will trigger the need for improvements of theoretical results. We do not intend to address modeling issues.
Rather we shall work with known models. However, we will seek to break new ground and to obtain new insight on the problems
with innovative choices of objective functions, reformulations, introduction of non-standard constraints as well as a thorough
sensitivity analysis of the solutions.
Although the problems under consideration will be solved via direct and indirect methods using well known optimization software
(for example WORHP, IPOPTS, KNITRO, GPOS, to name but a few) and software based on Hamilton Jacobi equations (for exemple,
RJO, PRONTO), we hope to contribute on those numerical schemes with routines for automatic refinement of the mesh and to allow
the numerical verification of optimality and regularity conditions.

Project

In search for innovative solutions for generating power from renewable energy, namely to extract wind energy at high altitudes, the University of Porto is starting the project UPWIND in the area of Airborne Wind Energy Systems (AWES).
In the area of AWES, there are open research questions, involving challenging optimization and control issues. This project aims to contribute to answer some of these questions, namely:
- Identification, Modelling and Estimation of AWES;
- Optimization and Control of AWES;
- Multiple Kite Systems.
More info: www.upwind.pt

Project

The main challenge in the project is the study of water management problem as an optimal control problem using and/or developing mathematical tools within the followings subjects: statistics, mathematical modelling, numerical optimization and optimal control.
The main goals of this project are:
1. To formulate the problem of the irrigation system planning as an optimal control problem using mathematical modelling techniques, statistical tools and agronomic knowledge.
2. To solve the formulated problem using different numerical methods and considering an adaptive time-mesh refinement strategy, leading to results with higher accuracy and yet with lower overall computational time.
3. To characterize and/or validate the results obtained using the control theory and to develop optimal control tools in such a way that they are able to provide proper answers to the specificities of the problem, namely to deal with climatic unpredictable behaviour.
4. To develop software tools that may be implemented with low cost, and, that encompasses not only the determination of the evapotranspiration value, but also the percolation and runoff values. Thus the modelling of the real life problem should be as close as possible to reality.
5. To apply the ''software'' in two distinct main crops of campus of
Universidade de Trás-dos-Montes to test the numerical models developed and its implementation.

Research

Research Item (25)

- Jul 2018

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.

- Jun 2018

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 paper, 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.

- Feb 2018

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—and 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.

- Oct 2017

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.

- Jul 2017
- 2017 International Conference in Energy and Sustainability in Small Developing Economies (ES2DE)

- Jan 2017
- CONTROLO 2016

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.

- Oct 2016
- NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA–2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”

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.

- Sep 2015
- 2015 Portuguese Meeting on Optimal Control

During a surgical procedure the anaesthesia enables a patient to tolerate the painful and avoid movement responses as a result of a surgical stimuli. The loss of the capacity to move is obtained by the administration of muscle relaxants, e.g., atracurium or rocuronium and is monitored by the neuromuscular blockade (NMB) level. This level is measured from a muscle response at the hand of the patient evoked by a stimulation of the adductor pollicis muscle through supra maximal train-of-four stimulation of the ulnar nerve. More concretely, the NMB level corresponds to the first single response calibrated by a reference twitch, ranging between 100% (full muscular activity) and 0% (total paralysis). In the anaesthesia practice, an initial dose of anaesthetics are administered following standard dosing guidelines, the patient’s response is observed and adjustments are made to achieve the desired target level. In order, to automate this process, a control law to control the NMB level obtained by solving an optimal control problem (OCP) is presented here. The OCP is solved using numerically methods. The results obtained show that the NMB level achieves the desired level.

- Sep 2015

When using direct methods to solve continuous-time 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 and increasing uniformly the number of mesh nodes may lead to a more complex problem. We propose an adaptive time--mesh refinement algorithm, considering different levels of refinement and several mesh refinement criteria. Namely, we use information of the adjoint multipliers to decide where to refine further. This technique is here tested to solve two optimal control problems. One involving nonholonomic vehicles with state constraints which is characterized by having strong nonlinearities and by discontinuous controls; the other is also a nonlinear problem of a compartmental SEIR system. The proposed strategy leads to results with higher accuracy and yet with lower overall computational time, when compared to results obtained by meshes having equidistant spacing. We also 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.

- Jul 2015
- 2015 SIAM Conference on Control and Its Applications (CT15)

Optimal control theory has gained increasing importance in biomedical applications, e.g., in the automatic administration of anesthetics during general anesthesia. In this context, one of the features that needs to be monitored is the depth of anesthesia. This is usually achieved by the joint administration of hypnotics and analgesics. The depth of anesthesia is quantified by the bispectral index that varies between 97.7% and 0%. This index should usually be kept at a reference level between 40% and 60% during surgeries with general anesthesia. In this contribution, we consider an open-loop control strategy to achieve this goal. In order to determine a suitable controller, we formulate a nonlinear optimal control problem and we solve it 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.

- Jun 2015
- 23rd Mediterranean Conference on Control & Automation - MED 2015

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 preliminary but illustrate a good performance of this strategy when applied to biomedical problems.

- Nov 2014

An optimal control problem with state constraints based on a SEIR model to control the spreading of infectious diseases is consi- dered. 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.

- Nov 2014

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.

- Oct 2014

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. Copyright © 2013 John Wiley & Sons, Ltd.

- Aug 2014

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.

- Oct 2013
- AIP Conference Proceedings

Direct methods are becoming the most used technique to solve nonlinear
optimal control problems. Regular time meshes having equidistant spacing
are frequently used. However, in some cases these meshes cannot cope
accurately with nonlinear behavior. One way to improve the solution is
to select a new mesh with a greater number of nodes. Another way,
involves adaptive mesh refinement. In this case, the mesh nodes have non
equidistant spacing which allow a non uniform nodes collocation. In the
method presented in this paper, a time mesh refinement strategy based on
the local error is developed. After computing a solution in a coarse
mesh, the local error is evaluated, which gives information about the
subintervals of time domain where refinement is needed. This procedure
is repeated until the local error reaches a user-specified threshold.
The technique is applied to solve the car-like vehicle problem aiming
minimum consumption. The approach developed in this paper leads to
results with greater accuracy and yet with lower overall computational
time as compared to using a time meshes having equidistant spacing.

- Apr 2010
- EWEC 2010 ─ European Wind Energy Conference and Exhibition 2010

The analysis of turbulence intensity and wind shear factor, as in conventional wind resource measurements, showed a similar trend for both variables as a function of the wind speed. Although for the turbulence intensity, the wind speed of 15 ms-1 is generally regarded as the value at which its behaviour is asymptotic, there is no similar criterion defined for the shear factor. This work presents an alternative criterion for determining the wind speed at which the turbulence intensity must be referred to, which is also extended to and successfully tested in the case of the wind shear factor. This is the behaviour at high Reynolds number and can be well predicted by computer modelling of the wind flow equations over complex terrain.

- Dec 2009

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.

- Oct 2006
- Getting to know more, so as to act better

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 suitable 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.

- Apr 2006
- High Commissioner for Immigration and Ethnic Minorities

O livro PLANEAMENTO URBANO PARA A INTEGRAÇÃO DE IMIGRANTES visa caracterizar a situação actual dos imigrantes e das minorias étnicas na Área Metropolitana do Porto, bem como a respectiva evolução, no que se refere às suas características profissionais e de emprego, atributos habitacionais, e localização espacial da residência e do emprego, considerando cada um dos grupos populacionais de estrangeiros mais representativos nesta Área Metropolitana, e por comparação com as situações equivalentes dos portugueses residentes no mesmo espaço territorial. Desenvolveu-se um sistema de informação de gestão urbanística com interface cartográfico referente às variáveis profissionais e habitacionais, que possibilita a simulação de cenários alternativos de localização residencial e/ou de emprego, orientadoras da formulação de políticas urbanas concretas referentes à integração de imigrantes, por parte dos poderes públicos.