Design of optimal constrained dynamic compensators for non-stationary linear stochastic systems

Abstract

This paper deals with the design of fixed-order dynamic compensators for non-stationary linear stochastic systems with noisy observations, where the observation noise need not necessarily be white. An integral quadratic performance index defined over a finite time interval is employed and this yields a matrix variational problem in the compensator parameters. It is shown how the optimal, possibly time-varying, compensator parameters rnay be determined by direct solution of this variational problem using a conjugate-gradient technique. Consideration is also given to finding suboptimal compensators that are simpler to implement. In particular, an algorithm is proposed for designing compensators having gains that are constrained to be piecewise-constant functions of time, with provision for optimally choosing the instants at which gains changes occur. An illustrative numerical example is included.