Stability and control of linear stochastic systems with long-run average cost criterion

Author(s)

Alessandro do Nascimento Vargas

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação
• Defense date: 2009-06-30

Examining board members

João Bosco Ribeiro do Val; Oswaldo Luiz do Valle Costa; Marcelo Dutra Fragoso; Wagner Caradori do Amaral; José Cláudio Geromel

• Advisor: João Bosco Ribeiro do Val; Eduardo Fontoura Costa

Abstract

This monograph presents results on stability and control of stochastic systems represented by linear operators with respect to the state which are non-linear with respect to the control. The control seeks to optimize a long run average cost (LRAC). The control structure does not depend on the past history of the process and it can be used, in particular, to represent a broad range of control problems that appears in the literature. Regarding the stability, it is shown that the stochastic system is asymptotically stable in the mean if the LRAC is finite and if controllability and observability assumptions are satisfied. To guarantee the uniform second moment stability, some additional conditions must be verified. With respect to the control, the main goal is to assure the existence of an optimal stationary policy for the LRAC problem within the class of systems considered, and some independent conditions are derived. An approximation for the minimum LRAC is obtained, and it is illustrated numerically for the regulator problem of Markov jump linear systems, under the assumption that the controller does not have access to the Markov state. Numerical examples illustrate the derived theory. (AU)