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

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:70839

Pan, Z; Basar, T ^[1]

---

1. Univ. of Illinois, Urbana, IL (United States)

We study 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. We identify appropriate {open_quotes}slow{close_quotes} and {open_quotes}fast{close_quotes} 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 {epsilon} 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 {infinity}}-optimal control problem with measurement feedback, though this equivalence does not extend to the slow and fast subproblems arrived at after time-scale separation.

• DOE Contract Number: FG02-88ER13939
• OSTI ID: 70839
• Report Number(s): CONF-941216--
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
CONTROL SYSTEMS
DESIGN
MATHEMATICAL MODELS
OPTIMAL CONTROL
STOCHASTIC PROCESSES