Speakers/Abstracts

Confirmed speakers:


  • Agnieszka Malinowska, Bialystok University of Technology, Białystok, Poland

Title: OPTIMAL CONTROL OF FRACTIONAL MULTI-AGENT SYSTEMS

Abstract: We deal with control strategies for discrete-time fractional multi-agent systems. By using the discrete fractional order operator we introduce memory effects to the considered problem.Necessary optimality conditions for discrete-time fractional optimal control problems with single- and double-summator dynamics are proved. We demonstrate the validity of the proposed control strategy by numerical examples.


  • Amit Bhaya, Federal University of Rio de Janeiro, Brazil

Título: Optimal feedback control of cash balance dynamics via linear programming.

Resumo: The classical cash balance problem of optimizing working capital in the short term is formulated as a discrete-time optimal control problem of maximizing final wealth, which is the total capital in the cash and investment accounts, over a finite horizon, subject to nonnegativity constraints and the standard dynamics of cash flow, including transaction or transfer costs, between the two accounts. Given a cash flow stream to the cash account (positive, if it is a payment to be made; negative, if it is a deposit), it is shown that the optimal control problem can be reformulated and solved as a linear program, furnishing the optimal sequence of transfers from the cash to the investment account and viceversa. To improve on this open-loop solution, which also requires prior knowledge of the cash flow demand stream, it is shown next that the classical Miller-Orr three level threshold control policy that generates a (suboptimal) sequence of transfers, can be simplified to a closed-loop controller based on a single threshold or target level, which, moreover, can also be formulated as a linear programming problem, for a given target and cash flow demand stream. An output feedback control policy that determines cash transfers based only on the current cash flow demand and cash balance, by maintaining the latter at zero, is shown to be optimal.


  • Ana Pedro Lemos-Paião, CIDMA, University of Aveiro

Title: Optimal control theory: an important tool to stop the spread of cholera epidemics

Abstract: We propose and analyse several mathematical models for the transmission dynamics of some strains of the bacterium Vibrio cholerae, responsible for the cholera disease in humans. Different controls are considered with the purpose to obtain distinct optimal control problems. The analytical and numerical studies of such problems allow us to determine the best way to stop the spread of this disease.Such optimal control problems are applied to the cholera's epidemic of Haiti (2010-2011) and Yemen (2017-2018).


  • Conceição Rocha, CIDMA, University of Aveiro

Title: Noncatastrophic Convolutional Codes over Zpr [d].

Abstract: An important class of convolutional codes over finite fields are the noncatastrophic codes. We consider the more general set of convolutional codes over finite rings and we study the noncatastrophic codes in this set. In particular, we present a characterization of these codes and we study their distance properties.


  • Ewa Girejko, Bialystok University of Technology, Białystok, Poland

Title: ON CONSENSUS UNDER DoS ATTACK IN THE MULTIAGENT SYSTEMS

Abstract: During the presentation multiagent systems under Denial-of-Service (DoS) attack will be presented. It is assumed that the dynamics of each agent is defined on an arbitrary time scale and during attacks the adversaries can attack partial or all channels at any time. Based on sufficient conditions for the global exponential stability of switched systems we derive simple criteria that verify if the consensus is still achieved in the multiagent system under DoS attacks. The effectiveness of the theoretical results is illustrated by numerical examples.


  • Filipa Santana, CIDMA, University of Aveiro

Title: Constructions of Maximum Rank Distance convolutional codes

Abstract: Rank metric convolutional codes are a generalization of the linear rank metric codes and they are better suited to be used in multi-shot network coding.

The sum rank distance is a suitable measure of the error correction capability of these codes. A Singleton-like upper bound was found for this distance in [1] and the Maximum Rank Distance convolutional codes are the ones whose sum rank distance achieve this bound. In this talk we present new constructions of MRD convolutional codes.

[1]D. Napp, R. Pinto, J. Rosenthal, and P. Vettori. MRD rank metric convolutional codes. IEEE International Symposium on Information Theory (ISIT) 2017.


  • Luís Machado, University of Trás-os-Montes e Alto Douro (UTAD), Portugal

Title: Minimum energy curves to path planning

Abstract: Dynamics of autonomous underwater or aerial vehicles are substantially affected by the vehicle’s velocity and acceleration as well as by the resistance offered by the fluid environment to the moving vehicle. This resistance is characterized by a mechanical force called drag.

Our purpose here is to formulate trajectory planning on fluid environments as an optimization problem responsible for driving a vehicle from an initial position to a final target while minimizing acceleration and drag. The corresponding Euler-Lagrange equations will be derived. As we will see, the presence of the drag term increases substantially the complexity of the problem even when the problem is only posed on a Euclidean setting. To tackle these hurdles, a numerical optimization approach based on the discretization of the cost functional will be proposed and some of the numerical illustrations for some special curved spaces will be provided.

This work has been supported by OE - national funds of FCT/MCTES (PIDDAC) under project UID/EEA/00048/2019.


  • Marinho Lopes, Department of Engineering Mathematics, University of Bristol, UK; Cardiff University Brain Research Imaging Centre, Cardiff University, UK

Title: "Mathematical modelling of epilepsy and its applications in epilepsy surgery and epilepsy classification"

Abstract: Epilepsy is a chronic neurological disorder that affects about 1% of people worldwide. Both diagnosis and treatment can be challenging. In this talk I will present a mathematical framework that can be used to better interpret clinical data in order to improve epilepsy diagnosis and surgical treatment. The framework assesses the inherent propensity of brain networks inferred from clinical data to generate seizure activity. The validity of this approach has been shown by analysing intracranial EEG recordings from a database comprising 16 patients who have undergone epilepsy surgery [1,2], and by studying scalp EEG from a cohort of 38 individuals with genetic generalized epilepsy and mesial temporal lobe epilepsy [3].

[1] Lopes, M. A., Richardson, M. P., Abela, E., Rummel, C., Schindler, K., Goodfellow, M., & Terry, J. R. (2017). An optimal strategy for epilepsy surgery: Disruption of the rich-club?. PLoS computational biology, 13(8), e1005637.

[2] Lopes, M. A., Richardson, M. P., Abela, E., Rummel, C., Schindler, K., Goodfellow, M., & Terry, J. R. (2018). Elevated ictal brain network ictogenicity enables prediction of optimal seizure control. Frontiers in neurology, 9, 98.

[3] Lopes, M. A., et al. (2019). Revealing epilepsy type using a computational analysis of interictal EEG, accepted in Sci Rep.


  • Raquel Pinto, CIDMA, University of Aveiro

Title: Error correction for 2D convolutional codes

Abstract: In this talk we consider the error correction decoding of two-dimensional (2D) convolutional codes. 2D convolutional have been a subject of interest in the last years and their algebraic properties and distance properties have been investigated by many authors (e.g. [1,2]). However very little is known about the decoding of these codes. In [3] the authors study the decoding of 2D convolutional codes over the erasure channel and present a decoding algorithm, but there is not known decoding algorithm when we consider the q-ary symmetric channels where errors can occur.

We propose a decoding algorithm for 2D convolutional codes by splitting the codewords of the code as polynomials with support in the parallel lines to the axis {a (1,0): a >=0} (or {a (0,1): a >=0}).

[1] E. Fornasini, M.E. Valcher. Algebraic aspects of two-dimensional convolutional codes, IEEE Transactions on Information Theory, 40, 1994, 1068-1082.

[2] J.J. Climent, D. Napp, C. Perea, R. Pinto. Maximum Distance Separable 2D Convolutional Codes. IEEE Transactions on Information Theory, 62(2), 2016, 669-680.

[3] J.J. Climent, D. Napp, R. Pinto, R. Simões: Decoding of 2D convolutional codes over the erasure channel. Advances in Mathematics of Communication, 10(1), 2016, 179-193


  • Silvério Rosa , Instituto de Telecomunicações and Department of Mathematics, University of Beira Interior

Title: Modelling optimal control of HIV-AIDS with memory

Abstract: The main contribution of this study is to investigate a generalization of a mathematical SICA model, proposed in [1], using fractional differential equations to describe the dynamics of HIV-AIDS infection. The infection process is modeled by a general functional response and the memory effect is presented by the Caputo fractional derivative. A fractional optimal control system is formulated to determine the best strategy for minimizing the spread of the disease into the population and the necessary conditions for optimality are derived. The numerical results help to understand the HIV-AIDS dynamics. The cost-effectiveness analysis of the fractional model is carried out.

References

[1] E. M. Lotfi, M. Mahrouf, M. Maziane, C. J. Silva, D. F. M. Torres and N. Yousfi,

A minimal HIV-AIDS infection model with general incidence rate and application to

Morocco data, Stat. Optim. Inf. Comput. 7(3), 588-603, 2019.


  • Ricardo Pereira , CIDMA, University of Aveiro

Title: Towards a geometric theory for nD behaviors: conditioned invariance and detectability subspaces

Abstract: We introduce the definitions of observer, conditioned invariance and detectability subspaces for discrete multidimensional behavioral systems, based on our previous work for the continuous 1D case, as a step forward in the attempt to develop a geometric theory for nD behaviors.