| 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. |
| 关键词: Indefinite stochastic LQ control, discrete-time stochastic systems, generalized algebraic Riccati equation, linear matrix inequality, semidefinite programming |
| DOI： |
| Received:October 18, 2014Revised:July 10, 2015 |
| 基金项目: |
|
| Infinite horizon indefinite stochastic linear quadratic control for discrete-time systems |
| W. Zhang,Y. Li,X. Liu |
| (College of Electrical Engineering and Automation, Shandong University of Science and Technology,Qingdao Shandong 266590, China;College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao Shandong 266590, China) |
| Abstract: |
| 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. |
| Key words: Indefinite stochastic LQ control, discrete-time stochastic systems, generalized algebraic Riccati equation, linear matrix inequality, semidefinite programming |
