A Computational Approach to Optimal Control Problems with Almost Smooth Controls

Ying Zhang (), Zhao Zhang () and Yingtao Xu
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Ying Zhang: Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China
Zhao Zhang: Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China
Yingtao Xu: Xingzhi College, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2023, vol. 40, issue 01, 1-20

Abstract: In this paper, we consider a class of optimal control problems involving continuous control and state inequality constraints where the control is almost smooth. We first employ the control parametrization technique via approximating the control signal by a piecewise linear function. Then, we develop a time scaling transformation procedure for transforming the approximate problem into an equivalent problem that can be solved readily using conventional methods. On this basis, a novel exact penalty function method is constructed by appending penalized constraint violations to the cost function. The gradient formulas and convergent properties ensure that the transformed unconstrained optimal parameter selection problems can be solved by existing optimization algorithms or software packages. Finally, an example is solved showing the effectiveness and applicability of the approach proposed.

Keywords: Almost smooth control; control parametrization; piecewise linear function; time scaling transformation; exact penalty function (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0217595921400340

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