Pareto optimality in infinite horizon linear quadratic differential games

被引：48

作者：

Reddy, Puduru Viswanadha ^{[1
]}

Engwerda, Jacob Christiaan ^{[2
]}

机构：

[1] HEC Montreal, GERAD, Montreal, PQ H3T 2A7, Canada

[2] Tilburg Univ, Dept Econometr & OR, NL-5000 LE Tilburg, Netherlands

来源：

AUTOMATICA | 2013年 / 49卷 / 06期

关键词：

Pareto optimality; Infinite horizon optimal control; Linear quadratic differential games; SUFFICIENT CONDITIONS; MAXIMUM PRINCIPLE;

D O I：

10.1016/j.automatica.2013.03.004

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 article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal control problems with a special structure. Next, we show that if the dynamical system is controllable, certain transversality conditions hold true, and as a result all the Pareto candidates can be obtained by solving a weighted sum optimal control problem. Further, exploiting the linear structure we investigate the relationship between Pareto optimality and weighted sum minimization. Finally, for the scalar case, we present an algorithm to find all the Pareto optimal solutions assuming mild conditions on the control space. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：1705 / 1714

页数：10

共 37 条

[1]

Acemoglu D., 2008, INTRO MODERN EC GROW

[2] LINEAR SYSTEM OPTIMISATION WITH PRESCRIBED DEGREE OF STABILITY [J].

ANDERSON, BD ;

MOORE, JB .

PROCEEDINGS OF THE INSTITUTION OF ELECTRICAL ENGINEERS-LONDON, 1969, 116 (12) :2083-+

[3]

[Anonymous], SIAM J CONTROL

[4]

Aseev S. M., 2004, SIAM Journal on Control and Optimization, V43, P1094, DOI DOI 10.1137/S0363012903427518

[5]

Basar T, 1998, Dynamic Noncooperative Game Theory

[6] GEOMETRY OF PARETO EQUILIBRIA AND A MAXIMUM PRINCIPLE IN N-PERSON DIFFERENTIAL GAMES [J].

BLAQUIERE, A ;

WIESE, KE ;

JURICEK, L .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1972, 38 (01) :223-+

[7]

Carlson D. A., 1991, Infinite Horizon Optimal Control-Deterministic and Stochastic Systems, V2nd

[8]

Dockner EngelbertJ., 2001, DIFFERENTIAL GAMES E

[9]

Engwerda J., 2005, LQ dynamic optimization and differential games

[10] The regular convex cooperative linear quadratic control problem [J].

Engwerda, Jacob .

AUTOMATICA, 2008, 44 (09) :2453-2457

← 1 2 3 4 →