Symmetry Reduction of Optimal Control Systems

Details Symmetry Reduction of Optimal Control Systems Symmetry Reduction of Optimal Control Systems

2011-05-26

arxiv.org/abs/1105.5174v2

Mathematics

Optimization and Control

25 pages, 2 figures

Scientific paper

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. We first formulate symmetries in nonlinear control systems and then link them to the corresponding symmetries in optimal control of such systems. A symmetry in an optimal control system gives rise to a natural choice of a principal connection in this setting. We then apply reduction theory of Hamiltonian mechanics to the Pontryagin maximum principle to reduce the optimal control system; the principal connection plays a central role here. Our result synthesizes some previous works on symmetries and reduction of nonlinear control and optimal control systems. Affine and kinematic optimal control systems are of particular interest: We explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems.

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