ON THE SOLUTION OF DISCRETE-TIME MARKOVIAN JUMP LINEAR-QUADRATIC CONTROL-PROBLEMS

被引：74

作者：

ABOUKANDIL, H ^{[1
]}

FREILING, G ^{[1
]}

JANK, G ^{[1
]}

机构：

[1] RHEIN WESTFAL TH AACHEN,LEHRSTUHL MATH 2,D-52056 AACHEN,GERMANY

来源：

AUTOMATICA | 1995年 / 31卷 / 05期

关键词：

DISCRETE-TIME SYSTEMS; LINEAR SYSTEMS; OPTIMAL CONTROL; RICCATI EQUATIONS; MARKOVIAN;

D O I：

10.1016/0005-1098(94)00164-E

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A necessary and sufficient condition for the existence of a positive-semidefinite solution of the coupled algebraic discrete-time Riccati-like equation occurring in Markovian jump control problems is derived. By verifying a simple matrix inequality, it is shown that such a solution exists and can be obtained as a limit of a monotonic sequence. This leads to a straightforward numerical algorithm for the computation of the solution. An example is given to illustrate the proposed method.

引用

页码：765 / 768

页数：4

共 13 条

[1]

Bitmead R. R., 1991, RICCATI EQUATION, P263

[2] MONOTONICITY AND STABILIZABILITY PROPERTIES OF SOLUTIONS OF THE RICCATI DIFFERENCE EQUATION - PROPOSITIONS, LEMMAS, THEOREMS, FALLACIOUS CONJECTURES AND COUNTEREXAMPLES [J].

BITMEAD, RR ;

GEVERS, MR ;

PETERSEN, IR ;

KAYE, RJ .

SYSTEMS & CONTROL LETTERS, 1985, 5 (05) :309-315

[3] FEEDBACK-CONTROL OF A CLASS OF LINEAR DISCRETE SYSTEMS WITH JUMP PARAMETERS AND QUADRATIC COST CRITERIA [J].

BLAIR, WP ;

SWORDER, DD .

INTERNATIONAL JOURNAL OF CONTROL, 1975, 21 (05) :833-841

[4] RHO-STABILITY AND ROBUSTNESS - DISCRETE-TIME CASE [J].

BOURLES, H ;

JOANNIC, Y ;

MERCIER, O .

INTERNATIONAL JOURNAL OF CONTROL, 1990, 52 (05) :1217-1239

[5]

CHAN SW, 1984, IEEE T AUTOMAT CONTR, V29, P110, DOI 10.1109/TAC.1984.1103465

[6]

CHIZECK HJ, 1986, INT J CONTROL, V43, P213, DOI 10.1080/00207178608933459

[7] RICCATI-EQUATIONS IN OPTIMAL FILTERING OF NONSTABILIZABLE SYSTEMS HAVING SINGULAR STATE TRANSITION MATRICES [J].

DESOUZA, CE ;

GEVERS, MR ;

GOODWIN, GC .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1986, 31 (09) :831-838

[8] ON STABILIZING PROPERTIES OF SOLUTIONS OF THE RICCATI DIFFERENCE EQUATION [J].

DESOUZA, CE .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1989, 34 (12) :1313-1316

[9]

FREILING G, 1994, UNPUUB GENERALIZED R

[10] CONTROLLABILITY, OBSERVABILITY AND DISCRETE-TIME MARKOVIAN JUMP LINEAR QUADRATIC CONTROL [J].

JI, YD ;

CHIZECK, HJ .

INTERNATIONAL JOURNAL OF CONTROL, 1988, 48 (02) :481-498

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