Optimal instantaneous output-feedback controllers for discrete-time linear systems with inaccessible state

Abstract

This paper considers the problem of designing optimal instantaneous output—feedback controllers for a class of discrete-time linear time-invariant systems with inaccessible state. The performance index is taken to be the expectation, with respect to the initial state, of the standard quadratic one for the discrete-time regulator. Necessary conditions for optimality are derived and existence of an optimal solution is proven. Implementation of the optimal controller requires the solution of two non-linear matrix algebraic equations, for which a computational algorithm is presented. The design is illustrated by a simple numerical example.