Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls
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AbstractThis paper is concerned with an optimal stochastic Linear-quadratic (LQ) control problem in infinite time horizon, where the diffusion term in dynamics depends on both the state and the control variables. In contrast to the deterministic case, we allow the control and state weighting matrices in the cost functional to be indefinite. This leads to an indefinite LQ problem, which may still be well posed due to the deep nature of uncertainty involved. The problem gives rise to a stochastic algebraic Riccati equation (SARE), which is, however, fundamentally different from the classical algebraic Riccati equation as a result of the indefinite nature of the LQ problem. To analyze the SARE, we introduce linear matrix inequalities (LMI's) whose feasibility is shown to be equivalent to the solvability of the SARE, Moreover, we develop a computational approach to the SARE via a semidefinite programming associated with the LMI's. Finally, numerical experiments are reported to illustrate the proposed approach.
All Author(s) ListRami MA, Zhou XY
Journal nameIEEE Transactions on Automatic Control
Year2000
Month6
Day1
Volume Number45
Issue Number6
PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Pages1131 - 1143
ISSN0018-9286
eISSN1558-2523
LanguagesEnglish-United Kingdom
Keywordslinear matrix inequality; mean-square stability; Schur's lemma; semidefinite programming; stochastic algebraic Riccati equation; stochastic linear-quadratic (LQ) control
Web of Science Subject CategoriesAutomation & Control Systems; AUTOMATION & CONTROL SYSTEMS; Engineering; Engineering, Electrical & Electronic; ENGINEERING, ELECTRICAL & ELECTRONIC

Last updated on 2021-11-01 at 01:04