EVENTO
Finite Dimensional Optimal Linear Mean Square Filter for Continuous-Time Markovian Jump Linear Systems
Tipo de evento: Defesa de Dissertação de Mestrado
Stochastic differential equations with Markovian jump parameters constitute one of the most important class of hybrid dynamical systems, which has been extensively used for the modeling of dynamical systems which are subject to abrupt changes in their structure. The abrupt changes can be due, for instance, to abrupt environmental disturbances, component failure, volatility in economic systems, changes in subsystems interconnections, abrupt changes in the operation of a nonlinear plant, etc. This can be found, for instance, in aircraft control systems, robot systems, large flexible structure for space station, etc. We shall be particularly interested in the linear class which is dubbed in the literature as the class of Markov jump linear systems (MJLS). The jump mechanism is modeled by a Markov process, which is also known in the literature as the operation mode. The dissertation address the filtering problem of the operation mode for the class of MJLS. Previous result in the literature on this problem has been obtained by Wonham, which has shown the existence of an optimal nonlinear filter for this problem. The main hindrance with Wonhams result, in the context of the control problem with partial observation of operation mode, is that it introduces a great deal of nonlinearity in the Hamilton-Jacobi-Belman equation, which makes it difficult to get an explicit closed solution for the control problem. Motivated by this, the main contribution of this dissertation is to devise an optimal linear filter for the mode operation, which we believe could be more favorable in the solution of the control problem with partial observations. In addition, relying on Murayamas stochastic numerical method and the results of Yuan and Mao, we carry out simulation of Wonhams filter, and the one devised in the dissertation, in order to compare their performances.
Data Início: 24/02/2017 Hora: 11:00 Data Fim: 24/02/2017 Hora: 14:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio B
Aluno: Fortia Vila Verges - - LNCC
Orientador: Marcelo Dutra Fragoso - Laboratório Nacional de Computação Científica - LNCC
Participante Banca Examinadora: Adilson Arruda - - Jack Baczynski - Laboratório Nacional de Computação Científica - LNCC Marcelo Dutra Fragoso - Laboratório Nacional de Computação Científica - LNCC
Suplente Banca Examinadora: João Bosco Ribeiro do Val - Universidade Estadual de Campinas - UNICAMP Marcos Garcia Todorov - Laboratório Nacional de Computação Científica - LNCC
