Optimal control of longitudinal deformations of a thermoelastic rod with unilateral contact condition of the Signorini type

In this article, we study the optimal control for longitudinal deformations of a thermoelastic rod. The controlled system is equipped with unilateral contact condition of the Signorini type. By the Dubovitskii and Milyutin functional analytical approach, we derive the necessary optimality conditions for optimal control problems with equality and inequality constraints in both fixed and free final horizon cases. Finally, the applicability of the derived Pontryagin maximum principles is simply addressed in the conclusion.