General suboptimal approach to the control and estimation of discrete-time systems

Abstract

A general suboptimal approach to the finite-time control of linear discrete time systems is introduced. The approach is also valid, with appropriate modifications, for the dual case of finite-time suboptimal state estimation. The method entails the use of a moving cost criterion which is to be minimized. It provides the advantages of constant feedback gain, a minimum number of iterations to find the stabilizing solution, and an extra freedom of transient response adjustment. Asymptotic stability of the closed-loop system is proved for a large parameter class, and it is shown that stability is robust with an extent depending on the design parameters. A special doubling algorithm is proposed to compute the feedback gains. The degree of suboptimality of the controller with respect to the linear quadratic regulator is discussed.