Abstract
This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. We formulate symmetries in nonlinear control systems and then link it to symmetries in optimal control of such systems. We apply Poisson reduction to the Pontryagin maximum principle to reduce the optimal control system. Affine and kinematic optimal control systems are of particular interest: We show an example of kinematic optimal control to illustrate how the reduction simplifies optimal control systems.
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