Linear Stochastic Systems

Abstract

In this chapter, we study the stochastic optimal control of linear time invariant singularly perturbed and weakly coupled systems in both continuous and discrete-time domains. The main issue in the linear optimal stochastic control is the design of the optimal Kalman filter which has the same order as a dynamical system under consideration. In the case of large scale systems composed of slow, fast, and weakly coupled state variables, it is possible to replace the design of the global Kalman filters in terms of the reduced-order Kalman filters. In addition to these on-line simplifications, we also present the simplified calculations of the regulator and filter gains by using the corresponding parallel algorithms derived in Chapters 2 and 3.