Approximate maximum principle for discrete approximations of optimal control systems with nonsmooth objectives and endpoint constraints

Boris S. Mordukhovich; Ilya Shvartsman

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In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.