We study optimal control of problem governed by a coupled system of hemivariational inequality (HVI) and ordinary differential equation (ODE). The problem models viscoelastic, adhesive contact between a body and a foundation. We employ the Kelvin-Voigt viscoelastic law and consider the general nonmonotone and multivalued subdifferential boundary conditions. The bonding field at the contact surface changes according to ODE based law. We provide conditions which guarantee existence of optimal solutions for general Bolza type optimal control problem.
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