State and Output Gaussian Control of Discrete-Time Markov Jump Linear Systems with Horizon Defined by Stopping Times
Abstract
The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. In the model studied, the problem horizon is defined by an stopping time $\tau$ which represents either, the occurrence of a fix number N of failures or repairs, or the occurrence of a crucial failure event, after which the system paralyzed. From the constructive method used here a separation principle holds, andthe solutions are given in terms of a Kalman filter and a state feedback sequence of controls. The control gains are obtained by recursions from a set of algebraic Riccati equations for the former case or by a coupled set of algebraic Riccati equation for the latter case.
