Journal of the Operations Research Society of China >

2020 , Vol. 8 >Issue 4: 581 - 600

DOI: https://doi.org/10.1007/s40305-020-00299-5

The Time-Scaling Transformation Technique for Optimal Control Problems with Time-Varying Time-Delay Switched Systems

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  • 1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
    2 School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China

Received date: 2019-07-09

  Revised date: 2020-01-12

  Online published: 2020-12-29

Supported by

This work was supported by the National Natural Science Foundation of China (Nos.11871039 and 11771275).

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Abstract

In this paper, we consider a class of optimal control problems where the dynamical systems are time-delay switched systems with the delay being a function of time. By applying the control parameterization method, the control heights and switching times become decision variables that need to be optimized. It is well-known that, for this type problem, the variable switching times cannot be optimized directly. To work around this problem, we introduce a time-scaling transformation technique so that the original system is transformed an equivalent system, which is defined on a new time horizonwithfixedswitchingtimes.Basedontherelationshipbetweentheoriginaltime scale and the new time scale, we derive the gradients of the objective and constraint functions with respect to the control heights and durations. Then, the new problem can be solved by gradient-based optimization approach. To demonstrate the effectiveness of the time-scaling transformation technique, two example problems are solved.

Key words： Switched systems; The time-scaling transformation; Gradient-based optimization

Cite this article

Ning Zhang, Chang-Jun Yu, Fu-Sheng Xie . The Time-Scaling Transformation Technique for Optimal Control Problems with Time-Varying Time-Delay Switched Systems[J]. Journal of the Operations Research Society of China, 2020 , 8(4) : 581 -600 . DOI: 10.1007/s40305-020-00299-5

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