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 trainoffour 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 twodimensional
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 integerorder 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
SYSTECISR & 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
humanlike morphology is an important characteristic for these robots,
humanlike 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 goaldirected actions. In this talk we report
about the movement planning model for an anthropomorphic robot we have
developed that is inspired by the PostureBased Motion Planning Model
proposed by Rosenbaum and colleagues to explain human upper limb
movements. We present armhand movements of an anthropomorphic robot in
di.erent tasks and di.erent obstacle avoidance scenarios. The results
smooth, .uent and collisionfree 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 cellkill strategies
Abstract: This poster describes a study about optimal control applied to competing chemotherapeutic cellkill strategies. We use a generalised twoparameter 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 RamseyCassKoopmans 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 takeoff (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 highspeed 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 highspeed 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 turbinegenerator set under highly energetic seastate conditions was experimentally validated by means of tests performed in a PTO test rig using an hardware15 intheloop configuration. The OWC sparbuoy hydrodynamics, the turbine aerodynamics and the compressibility effects on the air chamber are numerically modelled in realtime for different seastate 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 L^{1}, 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 timemesh 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
SYSTECISR & 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 threedimensional 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 trajectorytracking and a
geometrictracking 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 tradeoff between
trajectorytracking and geometrictracking 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
trajectorytracking and geometrictracking optimal control strategies.

SIMÃO P. S. SANTOS, Natália Martins, Delfim F. M. Torres
CIDMA, Universidade de Aveiro

Title: An optimal control approach to higherorder variational problems of Herglotz type
Abstract:
We approach higherorder 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 higherorder variational problems, valid for piecewise
smooth functions.

CRISTIANA J. SILVA, Paula Rodrigues, Delfim F. M. Torres
CIDMA, Universidade de Aveiro

Title: Optimal control and costeffectiveness 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 postexposure 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 costeffectiveness 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: Directmultisearch 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 blackbox type, preventing the use of
derivativebased techniques. We propose a novel multiobjective
derivativefree methodology which does not aggregate any of the
objective functions. Our framework is inspired by the search/poll
paradigm of directsearch 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. 


