The control parameterization method for nonlinear optimal control: A survey

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January 2014, 10(1): 275-309. doi: 10.3934/jimo.2014.10.275

The control parameterization method for nonlinear optimal control: A survey

Qun Lin ^1, , Ryan Loxton ^1, and Kok Lay Teo ^2,

1.	Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845
2.	Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U 1987, Perth, W.A. 6845

Received January 2013 Revised July 2013 Published October 2013

Abstract
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The control parameterization method is a popular numerical technique for solving optimal control problems. The main idea of control parameterization is to discretize the control space by approximating the control function by a linear combination of basis functions. Under this approximation scheme, the optimal control problem is reduced to an approximate nonlinear optimization problem with a finite number of decision variables. This approximate problem can then be solved using nonlinear programming techniques. The aim of this paper is to introduce the fundamentals of the control parameterization method and survey its various applications to non-standard optimal control problems. Topics discussed include gradient computation, numerical convergence, variable switching times, and methods for handling state constraints. We conclude the paper with some suggestions for future research.

Keywords: switching times, time-scaling transformation, control parameterization, Optimal control, state constraints..

Mathematics Subject Classification: Primary: 49M37; Secondary: 65K10, 65P99, 90C30, 93C1.

Citation: Qun Lin, Ryan Loxton, Kok Lay Teo. The control parameterization method for nonlinear optimal control: A survey. Journal of Industrial & Management Optimization, 2014, 10 (1) : 275-309. doi: 10.3934/jimo.2014.10.275

References:

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References:

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[26]	C. Y. Kaya and J. L. Noakes, Computational method for time-optimal switching control,, Journal of Optimization Theory and Applications, 117 (2003), 69. doi: 10.1023/A:1023600422807. Google Scholar
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[32]	H. W. J. Lee and K. H. Wong, Semi-infinite programming approach to nonlinear time-delayed optimal control problems with linear continuous constraints,, Optimization Methods and Software, 21 (2006), 679. doi: 10.1080/10556780500142306. Google Scholar
[33]	R. Li, K. L. Teo, K. H. Wong and G. R. Duan, Control parameterization enhancing transform for optimal control of switched systems,, Mathematical and Computer Modelling, 43 (2006), 1393. doi: 10.1016/j.mcm.2005.08.012. Google Scholar
[34]	B. Li, C. J. Yu, K. L. Teo and G. R. Duan, An exact penalty function method for continuous inequality constrained optimal control problem,, Journal of Optimization Theory and Applications, 151 (2011), 260. doi: 10.1007/s10957-011-9904-5. Google Scholar
[35]	B. Li, K. L. Teo, C. C. Lim and G. R. Duan, An optimal PID controller design for nonlinear constrained optimal control problems,, Discrete and Continuous Dynamical Systems: Series B, 16 (2011), 1101. doi: 10.3934/dcdsb.2011.16.1101. Google Scholar
[36]	Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, A new computational method for a class of free terminal time optimal control problems,, Pacific Journal of Optimization, 7 (2011), 63. Google Scholar
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