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A computational method for solving time-delay optimal control problems with free terminal time

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2014
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Journal Article

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Liu, C. and Loxton, R. and Teo, K.L. 2014. A computational method for solving time-delay optimal control problems with free terminal time. Systems and Control Letters. 72: pp. 53-60.
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Systems and Control Letters
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Department of Mathematics and Statistics
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NOTICE: This is the author’s version of a work that was accepted for publication in Systems and Control Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Systems and Control Letters, Vol. 72, (2014). doi: 10.1016/j.sysconle.2014.07.001

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Abstract

This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system (which influences the variable time delays in the new system). We develop a gradient-based optimization approach for solving this approximate problem. Simulation results are also provided to demonstrate the effectiveness of the proposed approach.