Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T10:11:52.510Z Has data issue: false hasContentIssue false
  • English
  • Français

OPTIMAL CONTROL OF SWITCHED IMPULSIVE SYSTEMS WITH TIME DELAY

Published online by Cambridge University Press:  07 February 2013

K. H. WONG  and
W. M. TANG
K. H. WONG*
Affiliation:
College of Computer and Information Science, Chongqing Normal University, Chongqing 400047, China
W. M. TANG*
Affiliation:
College of Computer and Information Science, Chongqing Normal University, Chongqing 400047, China
*
✉karwong01@gmail.com
✉cqtwm@163.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We develop a computational method for solving an optimal control problem governed by a switched impulsive dynamical system with time delay. At each time instant, only one subsystem is active. We propose a computational method for solving this optimal control problem where the time spent by the state in each subsystem is treated as a new parameter. These parameters and the jump strengths of the impulses are decision parameters to be optimized. The gradient formula of the cost function is derived in terms of solving a number of delay differential equations forward in time. Based on this, the optimal control problem can be solved as an optimization problem.

Keywords

switched and impulsive systemstime delaysubsystemsmagnitudes of impulsesduration timesmathematical programming problem
Type
Research Article
Information
The ANZIAM Journal , Volume 53 , Issue 4 , April 2012 , pp. 292 - 307
Copyright
Copyright ©2013 Australian Mathematical Society

References

Gao, R., Liu, X. and Yang, J., “On optimal control of a class of impulsive switching systems with terminal states constraints”, Nonlinear Anal. Theory Methods Appl. 73 (2010) 1940–1951; doi:10.1016/j.na.2010.05.013.CrossRefGoogle Scholar
Guan, Z. H., Hill, D. J. and Shen, X., “On hybrid impulsive and switching systems and application to nonlinear control”, IEEE Trans. Automat. Control 50 (2005) 1058–1062; doi:10.1109/TAC.2005.851462.CrossRefGoogle Scholar
Hu, J., Wang, H., Liu, X. and Liu, B., “Optimization problems for switched systems with impulsive control”, J. Control Theory Appl. 3 (2005) 93–100; doi:10.1007/s11768-005-0067-5.CrossRefGoogle Scholar
Jiang, C., Teo, K. L., Loxton, R. and Duan, G. R., “A neighboring extremal solution for an optimal switched impulsive control problem”, J. Indust. Manag. Optim. 8 (2012) 591–609; doi:10.3934/jimo.2012.8.591.Google Scholar
Kaya, C. Y. and Noakes, J. L., “Computational method for time-optimal switching control”, J. Optim. Theory Appl. 117 (2003) 69–92; doi:10.1023/A:1023600422807.CrossRefGoogle Scholar
Li, R., Feng, Z. G., Teo, K. L. and Duan, G. R., “Optimal piecewise state feedback control for impulsive switched systems”, Math. Comput. Modelling 48 (2008) 468–479; doi:10.1016/j.mcm.2007.06.028.CrossRefGoogle Scholar
Lin, Q., Loxton, R., Teo, K. L. and Wu, Y. H., “A new computational method for optimizing nonlinear impulsive systems”, Dyn. Contin. Discrete Impuls. Syst. Ser. B 18 (2011) 59–76.Google Scholar
Liu, C. Y., Gong, Z. H., Feng, E. M. and Yin, H. C., “Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture”, J. Indust. Manag. Optim. 5 (2009) 835–850; doi:10.3934/jimo.2009.5.835.CrossRefGoogle Scholar
Rui, G., “Towards optimal control problems of hybrid impulsive and switching systems with free terminal states”, Chinese J. Electronics 19 (2010) 557–562.Google Scholar
Verriest, E. I., “Regularization method for optimally switched and impulsive systems with biomedical applications”, in: Proc. 42nd IEEE Conf. on Decision and Control, 2003, 2156– 2161; doi:10.1109/CDC.2003.1272937.CrossRefGoogle Scholar
Verriest, E. I., “Optimal control for switched point delay systems with refractory period”, in: Proc. 16th IFAC World Congress, 2005.CrossRefGoogle Scholar
Verriest, E. I., “Optimal control for switched distributed delay systems with refractory period”, in: Proc. 44th IEEE Conf. on Decision and Control, 2005, 1421–1426; doi:10.1109/CDC.2005.1582358.CrossRefGoogle Scholar
Verriest, E. I., Delmotte, F. and Egerstedt, M., “Optimal impulsive control for point delay systems with refractory period”, in: Proc. 5th IFAC Workshop on Time Delay Systems, 2004.Google Scholar
Wu, C., Teo, K. L., Li, R. and Zhao, Y., “Optimal control of switched systems with time delay”, Appl. Math. Lett. 19 (2006) 1062–1067; doi:10.1016/j.aml.2005.11.018.CrossRefGoogle Scholar
Wu, C. Z., Teo, K. L. and Volker, R., “Optimal control of switched system with time delay detection of switching signal”, in: Numerical linear algebra in signals, systems and control, Volume 80 of Lecture Notes in Electrical Engineering (eds Van Dooren, P. et al. ), (Springer, Dordrecht, 2001), 467–478; doi:10.1007/978-94-007-0602-6_21.Google Scholar
Yin, Y., Zhao, J. and Liu, Y., “H-infinity control for switched and impulsive singular systems”, J. Control Theory Appl. 6 (2008) 86–92; doi:10.1007/s11768-008-6140-0.CrossRefGoogle Scholar