Regulation of Markov Jump Linear Systems Subject to Polytopic Uncertainties

Autor(es)

Bueno, Jose Nuno A. D. ; Marcos, Lucas B. ; Rocha, Kaio D. T. ; Terra, Marco H.

• Tipo de documento: Artigo Científico
• Fonte: IEEE Transactions on Automatic Control; v. 67, n. 11, p. 8-pg., 2022-11-01.

Resumo

When discrete-time Markov jump linear systems are prone to the damaging effects of polytopic uncertainties, it is necessary to address all the vertices of each Markov mode in order to properly design robust controllers. To this end, we propose a robust recursive linear-quadratic regulator for this class of systems. We define a quadratic min-max optimization problem by combining least-squares and penalty functions in a unified framework. We design a one-step cost function to encompass the entire set of vertices of each mode altogether, while maintaining its quadratic structure and the convexity of the problem. The solution is then obtained recursively and does not require numerical optimization packages. We establish conditions for convergence and stability by extending the matrix structure of the recursive solution. In addition, we provide numerical and real-world application examples to validate our method and to emphasize recursiveness and diminished computational effort. (AU)

• Processo FAPESP: 14/50851-0 - INCT 2014: Instituto Nacional de Ciência e Tecnologia para Sistemas Autônomos Cooperativos Aplicados em Segurança e Meio Ambiente
• Beneficiário: Marco Henrique Terra
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 21/08103-0 - Controle de sistemas veiculares heterogêneos autônomos e cooperativos
• Beneficiário: Lucas Barbosa Marcos
• Modalidade de apoio: Bolsas no Brasil - Programa Capacitação - Treinamento Técnico
• Processo FAPESP: 17/16346-4 - Controle tolerante a falhas de rede de comunicação para o movimento coordenado de robôs heterogêneos
• Beneficiário: Kaio Douglas Teófilo Rocha
• Modalidade de apoio: Bolsas no Brasil - Doutorado Direto