LONG TIME VERSUS STEADY STATE OPTIMAL CONTROL

被引：85

作者：

Porretta, Alessio ^{[1
]}

Zuazua, Enrique ^{[2
,3
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] BCAM, E-48009 Bilbao, Spain

[3] Basque Fdn Sci, Ikerbasque, Bilbao 48011, Spain

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2013年 / 51卷 / 06期

关键词：

optimal control problems; long time behavior; controllability; observability; MEAN-FIELD GAMES; DIMENSIONAL CONTROL-PROBLEMS; CONTROLLABILITY; EXISTENCE; EQUATIONS; AVERAGE; SYSTEM;

D O I：

10.1137/130907239

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper analyzes the convergence of optimal control problems for an evolution equation in a finite time-horizon [0, T] toward the limit steady state ones as T -> infinity. We focus on linear problems. We first consider linear time-independent finite-dimensional systems and show that the optimal controls and states exponentially converge in the transient time (as T tends to infinity) to the ones of the corresponding steady state model. For this to occur suitable observability assumptions need to be imposed. We then extend the results to infinite-dimensional systems including the linear heat and wave equations with distributed controls.

引用

页码：4242 / 4273

页数：32

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