Robust recursive frameworks for discrete-time linear systems subject to polytopic uncertainties

• Autor(a) principal: Bueno, José Nuno Almeida Dias
• Data de Publicação: 2023
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/18/18153/tde-02082023-084309/
• topic: algebraic Riccati equations; controle robusto; discrete-time linear systems; equações algébricas de Riccati; incertezas politópicas; linear quadratic regulator; Markov jump systems; optimization; otimização; polytopic uncertainties; regulador quadrático linear; robust control; sistemas lineares discretos; sistemas sujeitos a saltos Markovianos

The linear quadratic regulation problem for discrete-time systems has been subjected to research since its first appearance in the literature in the 1960s. Thereafter, different formulations and applications came to light to accommodate a wide range of theoretical and practical cases, such as systems undergoing the effects of unknown parametric variations. More specifically, in this thesis, we investigate the quadratic regulation problem for discrete-time linear and Markov jump linear systems subject to polytopic uncertainties. We define the problems regarding min-max optimization based on regularized least squares with uncertain data and penalty functions. We consider the cases where uncertainties affect the model matrices and transition probabilities and Markov jumps systems with unobserved chains. For each scenario, we designed a quadratic cost function to take all polytopic vertices into account in a unified manner while keeping the optimization problems\' convexity. The recursive solutions yield robust state feedback gains with a relatively lower computational burden if compared, for instance, with linear matrix inequalities approaches. By expanding the matrix structures of the solutions, we achieved equivalent reduced forms that are more adequate for convergence and stability analyses based on algebraic Riccati equations. Then, provided that some detectability and stabilizability conditions hold, the feedback gains ensure the stability of the associated closed-loop systems. The proposed method requires no further parameter tuning during operation, which is desirable in embedded applications and in systems with many vertices and Markov modes. Furthermore, we provide numerical and application examples to validate our results