Monotonicity of algebraic Lyapunov iterations for optimal control of jump parameter linear systems

被引：26
作者：
Gajic, Z
Losada, R
机构：
[1] Rutgers State Univ, Dept Elect & Comp Engn, Piscataway, NJ 08854 USA
[2] Math Works Inc, Natick, MA 01760 USA
来源：
SYSTEMS & CONTROL LETTERS | 2000年 / 41卷 / 03期
关键词：
coupled algebraic Riccati equations; Lyapunov equation; parallel computation; stochastic control; stochastic jump processes;
D O I：
10.1016/S0167-6911(00)00051-7
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper we show that the sequences of the solutions of the decoupled algebraic Lyapunov equations are monotonic under proper initialization. These sequences converge from above to the positive-semidefinite stabilizing solutions of the system of coupled algebraic Riccati equations of the optimal control problem of jump parameter linear systems. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：175 / 181
页数：7
相关论文
共 17 条
[1]   SOLUTION AND ASYMPTOTIC-BEHAVIOR OF COUPLED RICCATGI EQUATIONS IN JUMP LINEAR-SYSTEMS [J].
ABOUKANDIL, H ;
FREILING, G ;
JANK, G .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1994, 39 (08) :1631-1636
[2]   MINIMAX CONTROL OF SWITCHING SYSTEMS UNDER SAMPLING [J].
BASAR, T .
SYSTEMS & CONTROL LETTERS, 1995, 25 (05) :315-325
[3]   PARALLEL COMPUTATION OF THE SOLUTIONS OF COUPLED ALGEBRAIC LYAPUNOV EQUATIONS [J].
BORNO, I .
AUTOMATICA, 1995, 31 (09) :1345-1347
[4]   Efficient solution of linearly coupled Lyapunov equations [J].
Collins, EG ;
Hodel, AS .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1997, 18 (02) :291-304
[5]   Solutions for the linear-quadratic control problem of Markov jump linear systems [J].
do Val, JBR ;
Geromel, JC ;
Costa, OLV .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1999, 103 (02) :283-311
[6]   LYAPUNOV ITERATIONS FOR OPTIMAL-CONTROL OF JUMP LINEAR-SYSTEMS AT STEADY-STATE [J].
GAJIC, Z ;
BORNO, I .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1995, 40 (11) :1971-1975
[7]  
Gajic Z., 1995, Lyapunov Matrix Equation in System Stability and Control
[8]   CONTROLLABILITY, STABILIZABILITY, AND CONTINUOUS-TIME MARKOVIAN JUMP LINEAR QUADRATIC CONTROL [J].
JI, YD ;
CHIZECK, HJ .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1990, 35 (07) :777-788
[9]  
Kantorovich LV., 1964, FUNCTIONAL ANAL NORM
[10]   ON AN ITERATIVE TECHNIQUE FOR RICCATI EQUATION COMPUTATIONS [J].
KLEINMAN, DL .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1968, AC13 (01) :114-+
12