Control and filtering for continuous-time Markov jump linear systems with partial mode information

• Autor(a) principal: Rodrigues , Caio César Graciani
• Data de Publicação: 2017
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/267
• topic: Processos estocásticos; Controle H-infinito; Filtragem H-infinito; Stochastic process; CNPQ::CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE::PROCESSOS ESTOCASTICOS ESPECIAIS

Over the past few decades, the study of systems subjected to abrupt changes in their structures has consolidated as a significant area of research, due, in part, to the increasing importance of dealing with the occurrence of random failures in complex systems. In this context, Markov jump linear system (MJLS) comes up as an approach of central interest, as a means of representing these dynamics. Among the numerous works that seek to establish design methods for control and filtering considering this class of systems, the scarcity of literature related to the partial observation scenarios is noticeable. This thesis features contributions to the H1 control and filtering for continuous-time MJLS with partial mode information. In order to overcome the challenge regarding the lack of information of the current state of the Markov chain, we use a detector-based formulation. In this formulation, we assume the existence of a detector, available at all times, which provides partial information about the operating mode of the jump process. A favorable feature of this strategy is that it allows us to recover (without being limited to) some recent results of partial information scenarios in which we have an explicit solution, such as the cases of complete information, mode-independent and cluster observations. Our results comprise a new bounded real lemma followed by the design of controllers and filters driven only by the informations given by the detector. Both, the H1 analysis and the design methods presented are established through the solutions of linear matrix inequalities. In addition, numerical simulations are also presented encompassing the H1 performance for particular structures of the detector process. From an application point of view, we highlight some examples related to the linearized dynamics for an unmanned aerial vehicle.