October  2006, 2(4): 435-450. doi: 10.3934/jimo.2006.2.435

Global impulsive optimal control computation

1. 

Department of Mathematics, Chongqing Normal University, Chongqing, China

2. 

Department of Mathematics and Statistics, Curtin University of Technology, Perth

Received  March 2006 Revised  August 2006 Published  October 2006

In this paper, we develop a global computational approach to a class of optimal control problems governed by impulsive dynamical systems and subject to continuous state inequality constraint. We show that this problem is equivalent to an optimal control problem governed by ordinary differential equations with periodic boundary conditions and subject to a set of the continuous state inequality constraints. For this equivalent optimal control problem, a constraint transcription method is used in conjunction with a penalty function to construct an appended new cost functional. This leads to a sequence of approximate optimal control problems only subject to periodic boundary conditions. Each of these approximate problems can be solved as an optimization problem using gradient-based optimization techniques. However, these techniques are designed only to find local optimal solutions. Thus, a filled function method is introduced to supplement the gradient-based optimization method. This leads to a combined method for finding a global optimal solution. A numerical example is solved using the proposed approach.
Citation: C.Z. Wu, K. L. Teo. Global impulsive optimal control computation. Journal of Industrial and Management Optimization, 2006, 2 (4) : 435-450. doi: 10.3934/jimo.2006.2.435
[1]

Canghua Jiang, Zhiqiang Guo, Xin Li, Hai Wang, Ming Yu. An efficient adjoint computational method based on lifted IRK integrator and exact penalty function for optimal control problems involving continuous inequality constraints. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1845-1865. doi: 10.3934/dcdss.2020109

[2]

Jérome Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control and Related Fields, 2013, 3 (2) : 185-208. doi: 10.3934/mcrf.2013.3.185

[3]

Alexander Arguchintsev, Vasilisa Poplevko. An optimal control problem by parabolic equation with boundary smooth control and an integral constraint. Numerical Algebra, Control and Optimization, 2018, 8 (2) : 193-202. doi: 10.3934/naco.2018011

[4]

Sofia O. Lopes, Fernando A. C. C. Fontes, Maria do Rosário de Pinho. On constraint qualifications for nondegenerate necessary conditions of optimality applied to optimal control problems. Discrete and Continuous Dynamical Systems, 2011, 29 (2) : 559-575. doi: 10.3934/dcds.2011.29.559

[5]

Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial and Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399

[6]

Térence Bayen, Alain Rapaport, Fatima-Zahra Tani. Optimal periodic control for scalar dynamics under integral constraint on the input. Mathematical Control and Related Fields, 2020, 10 (3) : 547-571. doi: 10.3934/mcrf.2020010

[7]

Zhen-Zhen Tao, Bing Sun. Galerkin spectral method for elliptic optimal control problem with $L^2$-norm control constraint. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021220

[8]

Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. A new exact penalty function method for continuous inequality constrained optimization problems. Journal of Industrial and Management Optimization, 2010, 6 (4) : 895-910. doi: 10.3934/jimo.2010.6.895

[9]

Nguyen Huy Chieu, Jen-Chih Yao. Subgradients of the optimal value function in a parametric discrete optimal control problem. Journal of Industrial and Management Optimization, 2010, 6 (2) : 401-410. doi: 10.3934/jimo.2010.6.401

[10]

Zhen-Zhen Tao, Bing Sun. Space-time spectral methods for a fourth-order parabolic optimal control problem in three control constraint cases. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022080

[11]

Chonghu Guan, Xun Li, Rui Zhou, Wenxin Zhou. Free boundary problem for an optimal investment problem with a borrowing constraint. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1915-1934. doi: 10.3934/jimo.2021049

[12]

Shihchung Chiang. Numerical optimal unbounded control with a singular integro-differential equation as a constraint. Conference Publications, 2013, 2013 (special) : 129-137. doi: 10.3934/proc.2013.2013.129

[13]

Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem. Journal of Industrial and Management Optimization, 2012, 8 (2) : 485-491. doi: 10.3934/jimo.2012.8.485

[14]

Hee-Dae Kwon, Jeehyun Lee, Sung-Dae Yang. Eigenseries solutions to optimal control problem and controllability problems on hyperbolic PDEs. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 305-325. doi: 10.3934/dcdsb.2010.13.305

[15]

Jingzhen Liu, Ka-Fai Cedric Yiu, Kok Lay Teo. Optimal investment-consumption problem with constraint. Journal of Industrial and Management Optimization, 2013, 9 (4) : 743-768. doi: 10.3934/jimo.2013.9.743

[16]

Vincenzo Basco, Piermarco Cannarsa, Hélène Frankowska. Necessary conditions for infinite horizon optimal control problems with state constraints. Mathematical Control and Related Fields, 2018, 8 (3&4) : 535-555. doi: 10.3934/mcrf.2018022

[17]

Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control and Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019

[18]

Xilu Wang, Xiaoliang Cheng. Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions. Evolution Equations and Control Theory, 2022  doi: 10.3934/eect.2021064

[19]

M. Delgado-Téllez, Alberto Ibort. On the geometry and topology of singular optimal control problems and their solutions. Conference Publications, 2003, 2003 (Special) : 223-233. doi: 10.3934/proc.2003.2003.223

[20]

Zhen-Zhen Tao, Bing Sun. Error estimates for spectral approximation of flow optimal control problem with $ L^2 $-norm control constraint. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022030

2020 Impact Factor: 1.801

Metrics

  • PDF downloads (253)
  • HTML views (0)
  • Cited by (37)

Other articles
by authors

[Back to Top]