Optimal control of Gao beam contact with double Signorini conditions

This paper investigates the optimal control problem associated with the dynamic frictionless contact process of a Gao beam, which incorporates double Signorini conditions. By employing the Dubovitskiĭ-Milyutin functional analytical approach, the necessary optimality conditions in the form of the Pontryagin maximum principle are derived for the case of fixed final time horizon. The analysis takes into account the nonsmooth characteristics of the contact constraints and provides a rigorous mathematical framework for describing optimal controls. The paper concludes with an algorithm highlighting the potential applications of the derived results.