ON THE OPTIMAL CONTROL OF BOOLEAN CONTROL NETWORKS

被引：79

作者：

Zhu, Qunxi ^{[1
,2
]}

Liu, Yang ^{[1
,3
]}

Lu, Jianquan ^{[3
]}

Cao, Jinde ^{[3
,4
,5
]}

机构：

[1] Zhejiang Normal Univ, Coll Math Phys & Informat Engn, Jinhua 321004, Peoples R China

[2] Fudan Univ, Coll Math Sci, Shanghai 200433, Peoples R China

[3] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China

[4] Nantong Univ, Sch Elect Engn, Nantong 226000, Peoples R China

[5] Shandong Normal Univ, Sch Math Sci, Jinan 250014, Shandong, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2018年 / 56卷 / 02期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Boolean control networks; Floyd algorithm; input-state transfer graph; optimal control; semitensor product; STATE-FEEDBACK STABILIZATION; CONTROLLABILITY; OPTIMIZATION; ALGORITHM; MATRICES; GAMES;

D O I：

10.1137/16M1070281

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 study the optimal control problem of Boolean control networks (BCNs). An optimal input-state transfer graph (OISTG) is defined for BCNs with cost in every stage. Optimal controllers are designed to minimize (or maximize) a given cost (or payoff) function over finite and/or infinite time horizon. In finite time horizon, a sufficient condition is derived for the optimal control problem, and an algorithm with the method of binary decomposition is proposed. Moreover, we prove the existence of optimal control for discounted problems over an infinite time horizon, and a new algorithm is presented to design corresponding optimal controllers. Compared with some existing methods, the new algorithm with OISTG can be used to reduce both space complexity and computational complexity in finding optimal controllers. Numerical examples are presented to illustrate the efficiency of the obtained results.

引用

页码：1321 / 1341

页数：21

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