Defesa Pública da Tese de Doutorado do Mestre em Engenharia Elétrica Daniel Denardi Huff, de acordo com os termos do convênio de cotutela entre a UFRGS e a Communauté Université Grenoble Alpes (UGA), França
Data: 14/12/2022 – quarta-feira
Horário: 10h00min
A defesa será realizada através da plataforma Zoom Meeting com acesso pelo link:
https://univ-grenoble-alpes-fr.zoom.us/j/99573229375?pwd=cVhEeW8xMG12SzR6OE1EbXBxUmhNdz09
Meeting ID: 995 7322 9375
Passcode: 070312
Banca Examinadora:
Prof. Dr. Laurentiu Hetel – Université de Lille, CNRS (Relator francês)
Centre de Recherche en Informatique, Signal et Automatique de Lille
Prof. Dr. Carlos Eduardo Trabuco Dórea – UFRN (Relator brasileiro)
Departamento de Engenharia de Computação e Automação
Profa. Dra. Sophie Tarbouriech – Laboratório LAAS, CNRS – França
Methods and Algorithms in Control, MAC group
Prof. Dr. Giorgio Valmorbida – CentraleSupelec – Laboratório L2S – França
Profa. Dra. Lucíola Campestrini – PPGEE -UFRGS
Prof. Dr. John-Jairo Martinez-Molina – Grenoble-INP – Laboratório GIPSA-Lab – França
Presidente da Banca: Prof. Dr. João Manoel Gomes da Silva Junior – PPGEE – UFRGS (Orientador brasileiro)
Prof. Dr. Mirko Fiacchini – GIPSA-LAB – UGA (Orientador francês)
Títle: “STABILITY ANALYSIS AND STABILIZATION OF LINEAR APERIODIC SAMPLED-DATA SYSTEMS SUBJECT TO INPUT CONSTRAINTS”
Abstract:
Motivated by the growing use of embedded controllers in different applications, where a communication protocol is responsible for the transmission of data between computer algorithms, actuators and sensors, the analysis and control design for sampled-data control systems have been addressed in many works. In this context, aperiodic sampling can be seen as a modeling abstraction employed to represent, in a theoretical framework, the effect of imperfections on the communication channel such as sampling jitters, fluctuations and, in some cases, packet dropouts. Moreover, due to physical limitations of actuators, input constraints and, in particular, input saturation are ubiquitous in real control problems. These constraints are source of nonlinear behaviors and performance degradation. In many cases, only local (or regional) stability of the closed-loop system can be ensured in the presence of actuators constraints and nonlinearities, even for linear plants. This work deals with linear aperiodic sampled-data systems where the control input, subject to constraints (e.g. saturation), is computed based on a feedback of the system state. It focuses on two main problems. The first one regards the stability analysis of the origin of such systems, with the determination of estimates of the region of attraction of the origin (RAO). The second one, in turn, corresponds to the control design, where a state-feedback control law is computed in order to enlarge an estimate of the RAO of the resulting closed-loop system. The proposed methods are based on the use of semidefiniteor linear programming and can therefore be easily applied in practice. One of the proposed methods considers a linear saturating feedback of the system state and quadratic Lyapunov functions, leading to ellipsoidal estimates of the RAO of the system. Two other methods deal with the stability analysis of the sampled-data systemsubject to input saturation providing polyhedral estimates of the RAO. Because of theirflexibility, adopting polyhedrons instead of ellipsoids allows a reduction of conservatism, but is very demanding in terms of computational complexity. Motivated by this fact, this thesis also proposes a control design method based on an alternative strategy, where the complexity of the polytopes is fixed a priori. This idea results in an optimization problem with bilinear constraints, where a stabilizing piecewise linear control law of relatively low complexity is found for the sampled-data system. The aforementioned methods consider a non-stochastic framework, where lower and upper bounds are imposed for the unknown, time-varying sampling interval of the system. As an additional contribution, this thesis also considers a stochastic setting. A control design method is proposed for the global stabilization in the mean square sense of the sampled-data system, where the linear feedback control law is subject to sector bounded nonlinearities and the sampling intervals are assumed to be random variables with the Erlang distribution. The possibility of packet dropouts is also explicitly taken into account through the Bernoulli distribution. Moreover, the proposed approach, which is based on the framework of Piecewise Deterministic Markov Processes, leads to non-conservative stabilization conditions in the unconstrained linear case.
Keywords: Sampled-data control, aperiodic sampling, random sampling, set invariance, ellipsoidal sets, polyhedral sets, region of attraction of the origin.”
