Optimal reduced-order compensation of time-varying discrete-time systems with deterministic and white parameters

Abstract

The finite-horizon optimal compensation problem is considered in the case of linear time-varying discrete-time systems with deterministic and white stochastic parameters and quadratic criteria. The dimensions of the compensator are a priori fixed and may be time varying. Also the dimensions of the system may be time varying. Strengthened discrete-time optimal projection equations (SDOPE) are developed which, within the class of minimal compensators, are equivalent to the first-order necessary optimality conditions. Based on the SDOPE and their associated boundary conditions, two numerical algorithms are presented to solve the two point boundary value problem. One is a homotopy algorithm while the second iterates the SDOPE repeatedly forward and backward in time. The latter algorithm is much more efficient and constitutes a generalization of the single iteration of the control and estimation Riccati equations, associated with the full-order problem for systems with deterministic parameters. The algorithms are illustrated with a numerical example. The case of systems with deterministic parameters will be treated as a special case of systems with white parameters.