A new computational strategy for optimal control problem with a cost on changing control

Yujing  Wang; Changjun  Yu; Kok Lay Teo

doi:10.3934/naco.2016016

Article Contents

2016, Volume 6, Issue 3: 339-364. Doi: 10.3934/naco.2016016

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A new computational strategy for optimal control problem with a cost on changing control

1.
Department of Mathematics and Statistics, Curtin University, Perth
2.
Department of Mathematics , Shanghai University, Shanghai

Received: March 31, 2015

Revised: August 31, 2016

Published: August 2016

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Abstract

In this paper, we consider a class of optimal control problems where the cost function is the sum of the terminal cost, the integral cost and the full variation of control. Here, the full variation of a control is defined as the sum of the total variations of its components. By using the control parameterization technique in conjunction with the time scaling transformation, we develop a new computational algorithm for solving this type of optimal control problem. Rigorous convergence analysis is provided for the new method. For illustration, we solve two numerical examples to show the effectiveness of the proposed method.

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Mathematics Subject Classification: Primary: 49J15, 34H05; Secondary: 93C95.

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