Employing the algebraic Riccati equation for the solution of the finite-horizon LQ problem

2004 ◽  
Author(s):  
A. Ferrante ◽  
G. Marro ◽  
L. Niogramatzidis
Keyword(s):  
Riccati Equation ◽  
Finite Horizon ◽  
Algebraic Riccati Equation ◽  
Lq Problem

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.

scholarly journals Indefinite LQ Problem for Irregular Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qingxiang Fang ◽  
Jigen Peng ◽  
Feilong Cao
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
Algebraic Riccati Equation ◽  
Closed Loop System ◽  
State Pair ◽  
Lq Problem ◽  
Control State

The indefinite LQ problem for irregular singular systems is investigated. Under some general conditions, the optimal control-state pair is obtained by solving an algebraic Riccati equation. The optimal control is synthesized as state feedback. All the finite poles of the closed-loop system are located on the left-half complex plane. An example is given to show the validity of the proposed conclusion.

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