The control parameterization method for nonlinear optimal control: A survey

Qun Lin; Ryan Loxton; Kok Lay Teo

doi:10.3934/jimo.2014.10.275

Article Contents

2014, Volume 10, Issue 1: 275-309. Doi: 10.3934/jimo.2014.10.275

This issue Previous Article Heuristics for parallel machine scheduling with batch delivery consideration Next Article Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation

The control parameterization method for nonlinear optimal control: A survey

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: December 31, 2012

Revised: June 30, 2013

Published: December 2013

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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.

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Mathematics Subject Classification: Primary: 49M37; Secondary: 65K10, 65P99, 90C30, 93C15.

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