Model simplification and optimal control of stochastic singularly perturbed systems under exponentiated quadratic cost

Abstract

Studies the optimal control of a class of stochastic singularly perturbed linear systems with noisy state measurements under positively and negatively exponentiated quadratic cost the so-called LEQG problem. The authors identify appropriate and subproblems, obtain their optimum solutions (compatible with the corresponding measurement structures), and subsequently study the performances they achieve on the full-order system as the singular perturbation parameter /spl epsiv/ becomes sufficiently small. A by-product of this analysis is a more direct derivation (than heretofore available) of the solution to the LEQG problem under noisy state measurements, which allows for a general quadratic cost (with cross terms) in the exponent and correlation between system and measurement noises. Such a general LEQG problem is encountered in the slow-fast decomposition of the full-order problem, even if the original problem does not feature correlated noises. In this general context, the paper also establishes a complete equivalence between the LEQG problem and the H/sup /spl infin//-optimal control problem with measurement feedback, though this equivalence does not extend to the slow and fast subproblems arrived at after time-scale separation. >