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

共 50 条

[21] Design method of optimal control schedule for the adaptive cycle engine steady-state performance [J].

Xu, Yihao ;

Tang, Hailong ;

Chen, Min .

CHINESE JOURNAL OF AERONAUTICS, 2022, 35 (04) :148-164

[22] An Analysis on the Time Optimal Control Results for Hilfer Fractional Hemivariational Inequalities [J].

Dhanush, A. ;

Vijayakumar, V. .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2025, 19 (06)

[23] Optimal Regional Tracking Control of Time-Fractional Diffusion Systems [J].

Ge, Fudong ;

Chen, YangQuan .

2021 AMERICAN CONTROL CONFERENCE (ACC), 2021, :2782-2787

[24] AN APPROACH TO THE OPTIMAL TIME FOR A TIME OPTIMAL CONTROL PROBLEM OF AN INTERNALLY CONTROLLED HEAT EQUATION [J].

Wang, Gengsheng ;

Zheng, Guojie .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2012, 50 (02) :601-628

[25] Stabilization, Controllability and Optimal Control of Boolean Networks With Impulsive Effects and State Constraints [J].

Chen, Hao ;

Li, Xingde ;

Sun, Jitao .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2015, 60 (03) :806-811

[26] Chemotaxis driven formation of time periodic pattern and steady state pattern [J].

Jin, Chunhua ;

Zhang, Xuping .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 370 :498-536

[27] Steady-State Operation Control of Gyrotrons in Support of Long Pulse Plasma Operation in EAST [J].

Xu, Weiye ;

Xu, Handong ;

Hu, Tao ;

Yang, Yong ;

Feng, Jianqiang ;

Hu, Huaichuan ;

Zhang, Jian ;

Li, Miaohui .

IEEE TRANSACTIONS ON NUCLEAR SCIENCE, 2023, 70 (06) :1143-1148

[28] SUFFICIENCY AND SENSITIVITY FOR NONLINEAR OPTIMAL CONTROL PROBLEMS ON TIME SCALES VIA COERCIVITY [J].

Hilscher, Roman Simon ;

Zeidan, Vera .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2018, 24 (04) :1705-1734

[29] On Optimal Time-Varying Feedback Controllability for Probabilistic Boolean Control Networks [J].

Toyoda, Mitsuru ;

Wu, Yuhu .

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2020, 31 (06) :2202-2208

[30] Hamilton-Jacobi-Bellman equations for optimal control processes with convex state constraints [J].

Hermosilla, Cristopher ;

Vinter, Richard ;

Zidani, Hasnaa .

SYSTEMS & CONTROL LETTERS, 2017, 109 :30-36

← 1 2 3 4 5 →