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Journal of Industrial and Management Optimization (JIMO)
 

The control parameterization method for nonlinear optimal control: A survey

Pages: 275 - 309, Volume 10, Issue 1, January 2014      doi:10.3934/jimo.2014.10.275

 
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Qun Lin - Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845, Australia (email)
Ryan Loxton - Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845, Australia (email)
Kok Lay Teo - Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U 1987, Perth, W.A. 6845, Australia (email)

Abstract: 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:  Optimal control, control parameterization, switching times, time-scaling transformation, state constraints.
Mathematics Subject Classification:  Primary: 49M37; Secondary: 65K10, 65P99, 90C30, 93C15.

Received: January 2013;      Revised: July 2013;      Available Online: October 2013.

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