Indefinite stochastic LQ control with cross term via semidefinite programming

2003 ◽  
Vol 13 (1-2) ◽  
pp. 85-97 ◽  
Author(s):  
Chengxin Luo ◽  
Enmin Feng
Keyword(s):  
Semidefinite Programming ◽  
Cross Term ◽  
Indefinite Stochastic Lq Control ◽  
Lq Control ◽  
Stochastic Lq Control

scholarly journals Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Hongli
Keyword(s):  
State Constraints ◽  
Terminal State ◽  
Equality Constraints ◽  
Necessary Condition ◽  
Mathematical Programming Problem ◽  
Lagrangian Multiplier ◽  
Lq Problem ◽  
Indefinite Stochastic Lq Control ◽  
Lq Control ◽  
Stochastic Lq Control

This paper studies the indefinite stochastic LQ control problem with quadratic and mixed terminal state equality constraints, which can be transformed into a mathematical programming problem. By means of the Lagrangian multiplier theorem and Riesz representation theorem, the main result given in this paper is the necessary condition for indefinite stochastic LQ control with quadratic and mixed terminal equality constraints. The result shows that the different terminal state constraints will cause the endpoint condition of the differential Riccati equation to be changed. It coincides with the indefinite stochastic LQ problem with linear terminal state constraint, so the result given in this paper can be viewed as the extension of the indefinite stochastic LQ problem with the linear terminal state equality constraint. In order to guarantee the existence and the uniqueness of the linear feedback control, a sufficient condition is also presented in the paper. A numerical example is presented at the end of the paper.

scholarly journals Indefinite LQ Control for Discrete-Time Stochastic Systems via Semidefinite Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Shaowei Zhou ◽  
Weihai Zhang
Keyword(s):  
Semidefinite Programming ◽  
Riccati Equation ◽  
Discrete Time ◽  
Time Horizon ◽  
Stochastic Systems ◽  
Positive Semidefinite ◽  
Algebraic Riccati Equation ◽  
Infinite Time ◽  
Lq Problem ◽  
Lq Control

This paper is concerned with a discrete-time indefinite stochastic LQ problem in an infinite-time horizon. A generalized stochastic algebraic Riccati equation (GSARE) that involves the Moore-Penrose inverse of a matrix and a positive semidefinite constraint is introduced. We mainly use a semidefinite-programming- (SDP-) based approach to study corresponding problems. Several relations among SDP complementary duality, the GSARE, and the optimality of LQ problem are established.

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