Near-optimum regulators for singularly perturbed systems with random parameters

A singular perturbation approach is presented to study systems that are subject to random parameters. A near-optimum state regulator is composed of two subsystem regulators (slow and fast regulators) with the matrix coefficients obtained from two reduced-order independent suboptimal control problems. The conditions for complete separation of slow and fast regulator designs are given. A recursive algorithm for the design of regulators with random parameters is also given. It is shown that the composite feedback control is O(ε) close to the optimal one, which yields an O(ε²) approximation of optimal performance