A gradient-type algorithm for a class of optimal control processes governed by hybrid dynamical systems

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A gradient-type algorithm for a class of optimal control processes governed by hybrid dynamical systems

Year : 2011

Source Title : IMA Journal of Mathematical Control and Information

Document Type :

Abstract

Advanced optimization techniques play a key role in various problems from the modern control engineering. Our contribution deals with a class of hybrid control systems and the associated optimal control problems. We study a specific type of non-stationary hybrid control processes with autonomous location transitions and propose a constructive gradient-based optimization method. In this paper, we use the celebrated Lagrange method, the technique of the reduced gradient and obtain the first-order necessary optimality conditions for the above class of hybrid optimal control problems. These optimality conditions are closely related to the corresponding variant of the hybrid maximum principle and can be used effectively as a part of optimization algorithms. Finally, we consider some numerical aspects of the developed theory and propose an implementable computational scheme. © 2011 The author.