H/sup ∞/-optimal control for singularly perturbed systems. II. Imperfect state measurements

Abstract

For pt.I, see ibid., vol. 29, no. 2, p 401-423 (1993). In this paper we study the H/sup /spl infin//-optimal control of singularly perturbed linear systems under general imperfect measurements, for both finite- and infinite-horizon formulations. Using a differential game theoretic approach, we first show that as the singular perturbation parameter (say, /spl epsiv/>0) approaches zero, the optimal disturbance attenuation level for the full-order system under a quadratic performance index converges to a value that is bounded above by (and in some cases equal to) the maximum of the optimal disturbance attenuation levels for the and subsystems under appropriate slow and fast quadratic cost functions, with the bound being computable independently of E and knowing only the and dynamics of the system. We then construct a controller based on the subsystem only and obtain conditions under which it delivers a desired performance level even though the dynamics are completely neglected. The ultimate performance level achieved by this slow controller can be uniformly improved upon, however, by a composite controller that uses some feedback from the output of the subsystem. We construct one such controller, via a two-step sequential procedure, which uses static feedback from the output and dynamic feedback from an appropriate output, each one obtained by solving appropriate /spl epsiv/-independent lower dimensional H/sup /spl infin//-optimal control problems under some informational constraints. We provide a detailed analysis of the performance achieved by this lower-dimensional /spl epsiv/-independent composite controller when applied to the full-order system and illustrate the theory with some numerical results on some prototype systems. >