On a Class of Optimal Control Problems with State Jumps |
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| Authors: | Y. Liu K. L. Teo L. S. Jennings S. Wang |
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| Affiliation: | (1) School of Mathematics and Statistics, Curtin University of Technology, Perth, Western Australia, Australia;(2) School of Mathematics and Statistics, Curtin University of Technology, Perth, Western Australia, Australia;(3) Department of Mathematics, University of Western Australia, Nedlands, Western Australia, Australia;(4) School of Mathematics and Statistics, Curtin University of Technology, Perth, Western Australia, Australia |
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| Abstract: | In this paper, we consider a class of optimal control problems in which the dynamical system involves a finite number of switching times together with a state jump at each of these switching times. The locations of these switching times and a parameter vector representing the state jumps are taken as decision variables. We show that this class of optimal control problems is equivalent to a special class of optimal parameter selection problems. Gradient formulas for the cost functional and the constraint functional are derived. On this basis, a computational algorithm is proposed. For illustration, a numerical example is included. |
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| Keywords: | Optimal control switching times state jumps transformations optimal parameter selection problem automatic differentiation |
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