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

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 “slow” and “fast” 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 ε 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^∞-optimal control problem with measurement feedback, though this equivalence does not extend to the slow and fast subproblems arrived at after time-scale separation