A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems

Changjun Yu (), Qun Lin (), Ryan Loxton (), Kok Lay Teo () and Guoqiang Wang ()
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Changjun Yu: Central South University
Qun Lin: Curtin University
Ryan Loxton: Curtin University
Kok Lay Teo: Curtin University
Guoqiang Wang: Shanghai University of Engineering Science

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 3, No 9, 876-901

Abstract: Abstract In this paper, we consider a class of nonlinear time-delay optimal control problems with canonical equality and inequality constraints. We propose a new computational approach, which combines the control parameterization technique with a hybrid time-scaling strategy, for solving this class of optimal control problems. The proposed approach involves approximating the control variables by piecewise constant functions, whose heights and switching times are decision variables to be optimized. Then, the resulting problem with varying switching times is transformed, via a new hybrid time-scaling strategy, into an equivalent problem with fixed switching times, which is much preferred for numerical computation. Our new time-scaling strategy is hybrid in the sense that it is related to two coupled time-delay systems—one defined on the original time scale, in which the switching times are variable, the other defined on the new time scale, in which the switching times are fixed. This is different from the conventional time-scaling transformation widely used in the literature, which is not applicable to systems with time-delays. To demonstrate the effectiveness of the proposed approach, we solve four numerical examples. The results show that the costs obtained by our new approach are lower, when compared with those obtained by existing optimal control methods.

Keywords: Time-delay; Optimal control; Control parameterization; Time-scaling transformation; Time-delay control system; Computational method for optimal control; 49J15; 49M37; 65K10 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-015-0783-z

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