Relaxation of optimal control problems to equivalent convex programs |
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Authors: | R.M Lewis R.B Vinter |
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Affiliation: | Department of Electrical Engineering, University of Newcastle, New South Wales, 2308, Australia;Department of Computing and Control, Imperial College of Science and Technology, London, SW7 2BZ, England |
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Abstract: | Relaxed controls induce convexity of the velocity sets in optimal control problems, permitting a general existence theory. Here we obtain complete convexity, of the set of control-trajectory pairs, by relaxing the problem constraints to admit certain measures on the product of the control and trajectory spaces. It is proved that these measures are just unit mixtures of control-trajectory pairs and that admitting them does not alter the minimum value of the control problems. This can be used to derive necessary and sufficient conditions for optimality of dynamic programming type. |
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