Optimal control of vibrations of two nonlinear Gao beams connected with a joint

This paper is concerned with optimal control of vibrations of two uniform elastic or viscoelastic nonlinear Gao beams that are connected with a joint. The dynamic contact is modelled with the Signorini non-penetration or unilateral conditions in which the stops are assumed to be perfectly rigid. By the Dubovitskii and Milyutin functional analytical approach, we derive the Pontryagin maximum principle for the optimal control problem with multiple equality and multiple inequality constraints in fixed final horizon case. A remark is made on how to use the obtained results in the case of a quadratic cost functional.