Sequential adaptive switching time optimization technique for maximum hands-off control problems

Author:

Lin Sida1,Meng Lixia1,Yuan Jinlong1,Wu Changzhi2,Li An3,Liu Chongyang45,Xie Jun6

Affiliation:

1. Department of Applied Mathematics, School of Science, Dalian Maritime University, Dalian 116026, China

2. Chongqing National Center for Applied Mathematics, Chongqing Normal University, Chongqing 404087, China

3. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

4. School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China

5. Yantai Key Laboratory of Big Data Modeling and Intelligent Computing, Yantai 264005, China

6. Department of Basics, PLA Dalian Naval Academy, Dalian 116018, China

Abstract

<abstract><p>In this paper, we consider maximum hands-off control problem governed by a nonlinear dynamical system, where the maximum hands-off control constraint is characterized by an $ L^{0} $ norm. For this problem, we first approximate the $ L^{0} $ norm constraint by a $ L^{1} $ norm constraint. Then, the control parameterization together with sequential adaptive switching time optimization technique is proposed to approximate the optimal control problem by a sequence of finite-dimensional optimization problems. Furthermore, a smoothing technique is exploited to approximate the non-smooth maximum operator and an error analysis is investigated for this approximation. The gradients of the cost functional with respect to the decision variables in the approximate problem are derived. On the basis of these results, we develop a gradient-based optimization algorithm to solve the resulting optimization problem. Finally, an example is solved to demonstrate the effectiveness of the proposed algorithm.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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