Abstracts

The book of abstracts is available at the link "Book of abstracts".  It has some features only available in PDF version.


The abstracts are listed in alphabetical order of speakers.


JULIANA ALMEIDA, Luís Tiago Paiva, Teresa Mendonça, Paula Rocha
Faculdade de Engenharia, Universidade do Porto

Title: NMB target level tracking based on an optimal control problem

Abstract: 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 OCP is formulated in the following way:

The results obtained show that the NMB level achieves the desired level. More details will be shown at the conference.
   
CARLOS BALSA, Sílvio M.A. Gama
Instituto Politécnico de Bragança

Title: A numerical approach to a control problem in passive tracer advection by point vortex flow

Abstract: Point vortices are singular solutions of the two-dimensional incompressible Euler equations. These solutions correspond to the limiting case where the vorticity is completely concentrated on a finite number of spatial points each with a prescribed strength/circulation. By definition, a passive tracer is a point vortex with zero circulation.
In our case, we consider the advection of one passive tracer by N point vortices in the unbounded plane. In this context, we present the formulation of certain number of control problems, as well as the results of some numerical experiments showing the existence of optimal controls for the cases of N = 1, N = 2, N = 3 and N = 4 vortices. More precisely, we look for the optimal trajectories that minimize the objective function that correspond to the energy expended in the control of the trajectories. The restrictions are due to (i) the ordinary differential equations that govern the displacement of the passive particle around the point vortices, (ii) the available time T to go from the initial position z0 to the final destination zf , and (iii) the maximum absolute value umax that is imposed on the control variables. The latter consist in staircase controls, i.e. the control is written as a .nite linear combination of characterisc functions on the real interval.
   
NUNO R. O. BASTOS, Ricardo Almeida, Delfim F. M. Torres
CIDMA, UA & Departamento de Matematica, ESTG, Instituto Politécnico de Viseu


Title: A discretization method to solve fractional variational problems with dependence on Hadamard derivatives

Abstract: In this talk we provide a fast and simple method to solve fractional variational problems with dependence on Hadamard fractional derivatives. Using a relation between the Hadamard fractional operator and a sum involving integer-order derivatives, we rewrite the fractional problem into a classical optimal control problem. The latter problem is then solved by application of standard numerical techniques. We illustrate the procedure with an example.
   
AMÉLIA CALDEIRA, Diogo Bastos, Maria do Rosário de Pinho
SYSTEC-ISR & FEUP, Universidade do Porto


Title: Application of model predictive control in dieting control

Abstract: Millions of people around the world suffer from too much weight. It is well known that, in general, overweight people consume more calories than they use.
Any dynamic mathematical model to approach the human metabolism and to integrate knowledge about how the human body responds in terms of weight to changes of diet and physical activity is complex.
In this work we test one such model.
Using a weight reference trajectory (to achieve weight loss) we compare data at the time of assessment with the initial estimates of weight loss in a specific time frame. We apply the MPC technique to alert and define a new plan from such point.
The weight reference trajectory is a patchwork reference trajectory. First we use a given weight reference trajectory. If, at the time of assessment, the real weight deviates from the reference one, the reference trajectory is replaced by the solution of optimal control problem.
   
ELIANA COSTA E SILVA, Estela Bicho, Wolfram Erlhagend, M. Fernanda Costa, Ruud Menlenbroeke
Centro Algoritmi, Universidade do Minho & CIICESI, ESTGF - Instituto Politécnico do Porto

Title: From human motor control to robot movement control

Abstract: Robots are becoming more and more part of our daily life. For this reason they must be able to achieve high levels of cooperation and communication in order to be accepted by potential human users. Although human-like morphology is an important characteristic for these robots, human-like movement is recognized as a key feature for meaningful and natural interactions since they allow the user to more easily interpret movements of the robot as goal-directed actions. In this talk we report about the movement planning model for an anthropomorphic robot we have developed that is inspired by the Posture-Based Motion Planning Model proposed by Rosenbaum and colleagues to explain human upper limb movements. We present arm-hand movements of an anthropomorphic robot in di.erent tasks and di.erent obstacle avoidance scenarios. The results smooth, .uent and collision-free movements that qualitatively re.ect main characteristics of hand and arm trajectories observed in experiments with humans.
   
M. MARGARIDA A. FERREIRA, G.V. Smirnov
Universidade do Porto, Faculdade de Engenharia


Title: Optimal control for a hydroelectric power station problem

Abstract: A control problem for a cascade of hydroelectric power stations is analysed.
The model considered is a simple version of real life problems in hydroelectric systems and its formulation involves indefinite quadratic cost, control constraints and also pure state constraints. Optimal trajectories for some particular cases are investigated.
   
FERNANDO A.C.C. FONTES, Luís Tiago Paiva
Faculdade de Engenharia, Universidade do Porto
Title: Optimal control and model predictive control of kite power systems

Abstract: We consider continuous–time optimal control and model predictive control problems of kite power systems [1]. Kite power systems (KPS) not only provide interesting and challenging optimal control problems, but are also a promising technology to exploit renewable energy for electrical energy production.
A KPS consists of a tethered kite flying in a crosswind direction, connected to a drum and an electrical generator on the ground. As the kyte pulls the tether, the wind energy at high altitude is transmitted to the ground by unwinding the cable around the drum and thereby driving the electrical generator.
The solution of the OCP is challenging: it is highly nonlinear, involves a nonholonomic systems and might have multiple local optima. To solve these problems we consider a time–mesh that is adaptively refined to achieve a desired error threshold. Details of this technique and its use in other nonlinear systems are stated in [2, 3].
The refinement algorithm is extended to solve a sequence of optimal control problems in a Model Predictive Control (MPC) scheme. In this extension, we consider a time–dependent stopping criterion for the mesh refinement algorithm with different levels by imposing a higher accuracy requirement in the initial parts of each horizon, which are more relevant in MPC. The use of adaptive refinement in real–time optimization schemes, such as MPC, enables the possibility of obtaining a solution even when the optimization has to be interrupted at an early stage.
References
[1] Luís Tiago Paiva, Fernando A.C.C.Fontes. Mesh–Refinement Strategies for Fast Optimal Control and Model Predictive
Control of Kite Power Systems. in The International Airborne Wind Energy Conference 2015, pp. 101, Delft, June 2015.
[2] Luís Tiago Paiva, Fernando A.C.C. Fontes. Adaptive Time–Mesh Refinement in Optimal Control Problems with State
Constraints. Discrete and Continuous Dynamical Systems, 35(9), pp. 4553–4572, September 2015.
[3] Luís Tiago Paiva. Numerical Methods in Optimal Control and Model Predictive Control. PhD thesis, PhD in Applied Mathematics, Universidade do Porto, December 2014. http://hdl.handle.net/10216/77537
   
ALEXANDRA M. S. GASPAR, Filipe C. Mena
Centro de Matemática, Universidade do Minho
Title: Chemotherapeutic cell-kill strategies

Abstract: This poster describes a study about optimal control applied to competing chemotherapeutic cell-kill strategies. We use a generalised two-parameter model and tools from dynamic programming to find the optimal strategy which minimises the tumor mass and the ammount of drug used during the treatment.
   
ALEXANDRA GAVINA, José Matos, Paulo B. Vasconcelos
Instituto Superior de Engenharia do Porto
Title: Tau method for the solution of economic growth models

Abstract: In this work the Tau method is adapted to solve economic growth models issued from optimal control problems. The aim is to tackle models of the form

where u'>0, u''<0, T∈[0, +∞ [ and f a nonlinear function.
The spectral Tau method is modified to accommodate nonlinear terms in f, the discount (exponential) factor and the residual τ in the differential equation. This residual is projected in an orthogonal polynomial basis and thus it satisfies some suitable minimization properties. Numerical computations to compute an approximate solution will be illustrated on the workhorse Ramsey-Cass-Koopmans model.
   
JOÃO C. C. HENRIQUES, L. M. C. Gato, A. F. O. Falcão, J. L. M. Lemos
IDMEC & IST, Universidade de Lisboa
Title: On optimal latching control for a floating oscillating water column wave energy converter

Abstract: An oscillating water 1 column (OWC) wave energy converter (WEC) consists on a fixed or floating air chamber structure open to the sea below the water surface. The waves action forces the oscillation of the water column, compressing and decompressing the air inside the camber. This motion can be used to drive an air turbine coupled to an electrical generator. Probably the great advantage of
OWC based WECs is the ability to control or dissipate any excess of available energy to the power take-off (PTO) system that may occur in medium to high energetic sea states. The control of the energy available to the PTO system can be performed using two types of valve configurations: a relief
valve installed in parallel with the turbine and/or a high-speed stop valve installed in series with the turbine. The objective of the present paper is to assess the performance of a new optimal control algorithm based on the operation of a high-speed stop valve. In normal sea state conditions, the
valve operates in latching mode. Under high energetic sea conditions, the control algorithm limits: i) the turbine available power, ii) the generator torque and power and iii) the turbine/generator set rotational speed. The control of the turbine-generator set under highly energetic sea-state conditions was experimentally validated by means of tests performed in a PTO test rig using an hardware15 in-the-loop configuration. The OWC spar-buoy hydrodynamics, the turbine aerodynamics and the compressibility effects on the air chamber are numerically modelled in real-time for different sea-state conditions. A motor/generator set simulate the PTO system. The experimental results allowed the dynamic behaviour of the PTO to be characterized and provided validation of the proposed control algorithms that ensure operation within safe limits.
   
FILIPA NUNES NOGUEIRA, M.d.R de Pinho
Universidade do Porto
Title: Optimal control for normalized SEIR model

Abstract: Here, optimal control techniques, with cost function of type L1, are used for defining vaccination policies in order to control a generic infectious disease, using a normalized SEIR model. The normalized SEIR model has the advantage of allow the study of the spread of the infectious diseases according to the population and diseases features, instead of the population dimension. The Maximum Principle is used in order to validate the numerical solutions obtained.
   
LUÍS TIAGO PAIVA, Fernando A.C.C. Fontes
Faculdade de Engenharia, Universidade do Porto
Title: An adaptive mesh refinement method for state constrained optimal control problems

Abstract: We consider continuous–time optimal control problems (OCP) and we solve them using a time–mesh that is adaptively refined to achieve a desired level of accuracy.
A major feature of our strategy is to guide the refinement procedure according to the local error of the dual variables as a refinement criterion. This error can be efficiently computed by comparing the solution of a linear differential equation system – the adjoint equation of the maximum principle – against the numerically obtained multipliers. Moreover, the proposed mesh–refinement strategy considers several refinement criteria in a multi–level scheme. Details of this technique and its use in other nonlinear systems are reported in [1, 2].
The refinement strategy provides results with high accuracy and yet keeping a lower overall computational time, when compared with the use of traditional meshes having equidistant–spacing in continuous–time OCP.
The benefits of using an adaptive time-mesh algorithm are strongly evident in highly nonlinear systems.
References
[1] Luís Tiago Paiva, Fernando A.C.C. Fontes. Adaptive Time–Mesh Refinement in Optimal Control Problems with State Constraints. Discrete and Continuous Dynamical Systems, 35(9), pp. 4553–4572, September 2015.
[2] Luís Tiago Paiva. Numerical Methods in Optimal Control and Model Predictive Control. PhD thesis, PhD in Applied Mathematics, Universidade do Porto, December 2014. http://hdl.handle.net/10216/77537
   
PAULO REBELO, SILVÉRIO ROSA
Universidade da Beira Interior
Title: Optimal control problems for a system of linear diffusion equations

Abstract: The aim of this paper is to present the solution to an optimal control problem for an homogeneous system of linear diffusion equations. This system can be interpreted as a very simple model of two interacting chemicals with prescribed values of the concentration in the boundary. The goal is to obtain a desired final distribution to one of the elements by imposing the control on the other. Two cases are considered (one with a "local" control and one with a distributed control).
   
ALESSANDRO RUCCO, António Pedro Aguiar, John Hauser
SYSTEC-ISR & FEUP, Universidade do Porto
Title: A virtual target approach for trajectory optimization of autonomous robotic vehicles

Abstract: The main aim of this talk is to present and discuss novel optimal control based methods for trajectory optimization of autonomous robotic vehicles. The highlighted contribution is part of a broader research work developed in the last years to design motion planning algorithms for single and multiple autonomous robotic vehicles in dynamic environments. Specifically, in this talk we provide a Virtual Target Vehicle (VTV) perspective for trajectory optimization of a general class of vehicles moving in either two or three-dimensional space in presence of external disturbances. Given a desired path with a specified desired orientation and velocity profile, our goal is to compute the (local) optimal feasible trajectory that “best approximates” the desired one. We tackle the optimal problem by proposing a trajectory-tracking and a geometric-tracking approach. Based on the PRojection Operator based Newton method for Trajectory Optimization (PRONTO), we develop a trajectory optimization strategy where the minimization of the L2 distance between actual and desired trajectories is the optimization goal. The proposed optimization strategy explicitly
takes into account the velocity of the virtual target to be tracked, thus i) improving the convergence of the solver to obtain the optimal feasible path, and ii) avoiding the singularities that occur in some maneuver regulation techniques described in the literature. Moreover, the proposed method allows us to introduce viable trade-off between trajectory-tracking and geometric-tracking algorithms. We provide numerical computations based on several testing scenarios. The numerical computations allows us to illustrate the benefits of our method and highlights the advantages and disadvantages of the proposed trajectory-tracking and geometric-tracking optimal control strategies.
 
SIMÃO P. S. SANTOS, Natália Martins, Delfim F. M. Torres
CIDMA, Universidade de Aveiro
Title: An optimal control approach to higher-order variational problems of Herglotz type

Abstract: We approach higher-order variational problems of Herglotz type from an optimal control point of view. Using optimal control theory, we derive a generalized Euler Lagrange equation, transversality conditions, DuBois Reymond necessary optimality condition and Noether's theorem for Herglotz's type higher-order variational problems, valid for piecewise smooth functions.
 
CRISTIANA J. SILVA, Paula Rodrigues, Delfim F. M. Torres
CIDMA, Universidade de Aveiro


Title: Optimal control and cost-effectiveness analysis for a tuberculosis model

Abstract: Tuberculosis prevention, diagnosis and treatment represents a worldwide scale challenge. We propose an optimal control problem that consists in analyzing how two tuberculosis post-exposure interventions should be implemented, for a certain time period, in order to reduce the number of active infected individuals, while controlling the intervention implementation costs. We introduce some summary measures to describe how the optimal solutions change when varying transmission intensity and protection against reinfection. A cost-effectiveness analysis is done, to compare the application of each of the control measures, separately or in combination.
   
A. ISMAEL F. VAZ, Ana Custódio, José Madeira, Luis N. Vicente
Departamento de produção e Sistemas, Escola de Engenharia, Universidade do Minho

Title: Direct-multisearch for multiobjective optimization

Abstract: In practical applications of optimization it is common to have several conflicting objective functions to optimize. Frequently, these functions are subject to noise or can be of black-box type, preventing the use of derivative-based techniques. We propose a novel multiobjective derivative-free methodology which does not aggregate any of the objective functions. Our framework is inspired by the search/poll paradigm of direct-search methods of directional type and uses the concept of Pareto dominance to maintain a list of nondominated points (from which the new iterates or poll centers are chosen). The aim of our method is to generate as many points in the Pareto frontier as possible from the polling procedure itself, while keeping the whole framework general enough to accommodate other disseminating strategies, in particular when using the (here also) optional search step. We prove under the common assumptions used in direct search for single optimization that at least one limit point of the sequence of iterates lies in the Pareto frontier. Computational results are reported on a test set of multiobjective problems, which show that our methodology has an impressive capability of generating the whole Pareto frontier even without using a search step. If time allows, a multiobjective optimal control problem, resulting from a practical application, is addressed.