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

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.
Citation: Hamid Reza Marzban, Hamid Reza Tabrizidooz. Solution of nonlinear delay optimal control problems using a composite pseudospectral collocation method. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1379-1389. doi: 10.3934/cpaa.2010.9.1379
[1]

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

[2]

M. Alipour, M. A. Vali, A. H. Borzabadi. A hybrid parametrization approach for a class of nonlinear optimal control problems. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2019037

[3]

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

[4]

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

[5]

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

[6]

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

[7]

Chao Deng, Haixiang Yao, Yan Chen. Optimal investment and risk control problems with delay for an insurer in defaultable market. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-17. doi: 10.3934/jimo.2019070

[8]

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 & Management Optimization, 2018, 14 (2) : 473-496. doi: 10.3934/jimo.2017056

[9]

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

[10]

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

[11]

Kobamelo Mashaba, Jianxing Li, Honglei Xu, Xinhua Jiang. Optimal control of hybrid manufacturing systems by log-exponential smoothing aggregation. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020100

[12]

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

[13]

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 & Continuous Dynamical Systems - A, 2011, 29 (2) : 505-522. doi: 10.3934/dcds.2011.29.505

[14]

Dariusz Idczak, Rafał Kamocki. Existence of optimal solutions to lagrange problem for a fractional nonlinear control system with riemann-liouville derivative. Mathematical Control & Related Fields, 2017, 7 (3) : 449-464. doi: 10.3934/mcrf.2017016

[15]

Bavo Langerock. Optimal control problems with variable endpoints. Conference Publications, 2003, 2003 (Special) : 507-516. doi: 10.3934/proc.2003.2003.507

[16]

Alberto Bressan, Yunho Hong. Optimal control problems on stratified domains. Networks & Heterogeneous Media, 2007, 2 (2) : 313-331. doi: 10.3934/nhm.2007.2.313

[17]

M'hamed Kesri. Structural stability of optimal control problems. Communications on Pure & Applied Analysis, 2005, 4 (4) : 743-756. doi: 10.3934/cpaa.2005.4.743

[18]

Piermarco Cannarsa, Hélène Frankowska, Elsa M. Marchini. On Bolza optimal control problems with constraints. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 629-653. doi: 10.3934/dcdsb.2009.11.629

[19]

T. Zolezzi. Extended wellposedness of optimal control problems. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 547-553. doi: 10.3934/dcds.1995.1.547

[20]

Divya Thakur, Belinda Marchand. Hybrid optimal control for HIV multi-drug therapies: A finite set control transcription approach. Mathematical Biosciences & Engineering, 2012, 9 (4) : 899-914. doi: 10.3934/mbe.2012.9.899

2018 Impact Factor: 0.925

Metrics

  • PDF downloads (14)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]