Infinite horizon indefinite stochastic linear quadratic control for discrete-time systems
Weihai ZHANG
Yan LI
Xikui LIU
摘要：This paper discusses discrete-time stochastic linear quadratic (LQ) problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefinite. The problem gives rise to a generalized algebraic Riccati equation (GARE) that involves equality and inequality constraints. The well-posedness of the indefinite LQ problem is shown to be equivalent to the feasibility of a linear matrix inequality (LMI). Moreover, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQ problem. All the optimal controls are obtained in terms of the solution to the GARE. Finally, we give an LMI-based approach to solve the GARE via a semidefinite programming.
机标关键词：algebraic Riccati equationsemidefinite programminglinear matrix inequalityinequality constraintslinear quadraticcost function
资助基金：the National Natural Science Foundation of China()the National Natural Science Foundation of China(61174078)the National Natural Science Foundation of China(61170054)the National Natural Science Foundation of China(61402265)
论文发表日期：2015-01-01
在线出版日期：2025-08-15（本平台首次上网日期，不代表文献的发表时间）
页数：8( 230-237 )
英文信息