On optimal control of a sweeping process coupled with an Ordinary differential equation
Abstract.
We study a special case of an optimal control problem governed by a differential
equation and a differential rate-independent variational inequality, both with given
initial conditions. Under certain conditions, the variational inequality can be reformulated
as a differential inclusion with discontinuous right-hand side. This inclusion is known as sweeping process.
We perform a discretization scheme and prove the convergence of optimal solutions of the discretized problems
to the optimal solution of the original problem. For the discretized problems we study the properties
of the solution map and compute its coderivative. Employing an appropriate chain rule, this enables us
to compute the subdifferential of the objective function and to apply a suitable optimization technique
to solve the discretized problems. The investigated problem is used to model a situation arising in the area
of queuing theory.
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