American Institute of Mathematical Sciences

Advanced
September  2010, 9(5): 1379-1389. doi: 10.3934/cpaa.2010.9.1379

Solution of nonlinear delay optimal control problems using a composite pseudospectral collocation method

Hamid Reza Marzban 1, and  Hamid Reza Tabrizidooz 2,

1. 

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 8415683111, Iran
2. 

Department of Mathematics, Faculty of Science, University of Kashan, Kashan, 8731751167, Iran

Received  September 2009 Revised  January 2010 Published  May 2010

We develop a composite collocation approximation scheme for the numerical solution of nonlinear delay optimal control problems. For this purpose, we present an extension and also modification for the Gauss pseudospectral method using the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss points. In this respect, we derive the corresponding operational matrix of derivative according to the weak representation of derivative operator. In order to demonstrate the applicability, efficiency and accuracy of the proposed method, we examine two illustrative examples.
Keywords: pseudospectral methods., hybrid functions, Lagrange polynomials, Delay optimal control problems.
Mathematics Subject Classification: Primary: 49M25; Secondary: 65D25, 65M7.
Citation: Hamid Reza Marzban, Hamid Reza Tabrizidooz. Solution of nonlinear delay optimal control problems using a composite pseudospectral collocation method. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1379-1389. doi: 10.3934/cpaa.2010.9.1379
[1]

M. Alipour, M. A. Vali, A. H. Borzabadi. A hybrid parametrization approach for a class of nonlinear optimal control problems. Numerical Algebra, Control and Optimization, 2019, 9 (4) : 493-506. doi: 10.3934/naco.2019037
[2]

Sébastien Court, Karl Kunisch, Laurent Pfeiffer. Hybrid optimal control problems for a class of semilinear parabolic equations. Discrete and Continuous Dynamical Systems - S, 2018, 11 (6) : 1031-1060. doi: 10.3934/dcdss.2018060
[3]

Zhong-Qing Wang, Ben-Yu Guo, Yan-Na Wu. Pseudospectral method using generalized Laguerre functions for singular problems on unbounded domains. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 1019-1038. doi: 10.3934/dcdsb.2009.11.1019
[4]

Z. Foroozandeh, Maria do rosário de Pinho, M. Shamsi. On numerical methods for singular optimal control problems: An application to an AUV problem. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2219-2235. doi: 10.3934/dcdsb.2019092
[5]

Martin Benning, Elena Celledoni, Matthias J. Ehrhardt, Brynjulf Owren, Carola-Bibiane Schönlieb. Deep learning as optimal control problems: Models and numerical methods. Journal of Computational Dynamics, 2019, 6 (2) : 171-198. doi: 10.3934/jcd.2019009
[6]

Xiaowei Pang, Haiming Song, Xiaoshen Wang, Jiachuan Zhang. Efficient numerical methods for elliptic optimal control problems with random coefficient. Electronic Research Archive, 2020, 28 (2) : 1001-1022. doi: 10.3934/era.2020053
[7]

Chunjuan Hou, Yanping Chen, Zuliang Lu. Superconvergence property of finite element methods for parabolic optimal control problems. Journal of Industrial and Management Optimization, 2011, 7 (4) : 927-945. doi: 10.3934/jimo.2011.7.927
[8]

Chao Deng, Haixiang Yao, Yan Chen. Optimal investment and risk control problems with delay for an insurer in defaultable market. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2563-2579. doi: 10.3934/jimo.2019070
[9]

Gastão S. F. Frederico, Delfim F. M. Torres. Noether's symmetry Theorem for variational and optimal control problems with time delay. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 619-630. doi: 10.3934/naco.2012.2.619
[10]

Changjun Yu, Lei Yuan, Shuxuan Su. A new gradient computational formula for optimal control problems with time-delay. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021076
[11]

Hai Huang, Xianlong Fu. Optimal control problems for a neutral integro-differential system with infinite delay. Evolution Equations and Control Theory, 2022, 11 (1) : 177-197. doi: 10.3934/eect.2020107
[12]

Kareem T. Elgindy. Optimal control of a parabolic distributed parameter system using a fully exponentially convergent barycentric shifted gegenbauer integral pseudospectral method. Journal of Industrial and Management Optimization, 2018, 14 (2) : 473-496. doi: 10.3934/jimo.2017056
[13]

Zhenyu Lu, Junhao Hu, Xuerong Mao. Stabilisation by delay feedback control for highly nonlinear hybrid stochastic differential equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4099-4116. doi: 10.3934/dcdsb.2019052
[14]

Wei Mao, Yanan Jiang, Liangjian Hu, Xuerong Mao. Stabilization by intermittent control for hybrid stochastic differential delay equations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 569-581. doi: 10.3934/dcdsb.2021055
[15]

Arthur Fleig, Lars Grüne. Strict dissipativity analysis for classes of optimal control problems involving probability density functions. Mathematical Control and Related Fields, 2021, 11 (4) : 935-964. doi: 10.3934/mcrf.2020053
[16]

Evelyn Herberg, Michael Hinze. Variational discretization of one-dimensional elliptic optimal control problems with BV functions based on the mixed formulation. Mathematical Control and Related Fields, 2022  doi: 10.3934/mcrf.2022013
[17]

Kobamelo Mashaba, Jianxing Li, Honglei Xu, Xinhua Jiang. Optimal control of hybrid manufacturing systems by log-exponential smoothing aggregation. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1711-1719. doi: 10.3934/dcdss.2020100
[18]

Wandi Ding. Optimal control on hybrid ODE Systems with application to a tick disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 633-659. doi: 10.3934/mbe.2007.4.633
[19]

Lihua Li, Yan Gao, Hongjie Wang. Second order sufficient optimality conditions for hybrid control problems with state jump. Journal of Industrial and Management Optimization, 2015, 11 (1) : 329-343. doi: 10.3934/jimo.2015.11.329
[20]

Maria do Rosário de Pinho, Ilya Shvartsman. Lipschitz continuity of optimal control and Lagrange multipliers in a problem with mixed and pure state constraints. Discrete and Continuous Dynamical Systems, 2011, 29 (2) : 505-522. doi: 10.3934/dcds.2011.29.505

2020 Impact Factor: 1.916

Tools

Metrics

  • PDF downloads (94)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy