Second-Order PDE Constrained Controlled Optimization Problems with Application in Mechanics

The present paper deals with a class of second-order PDE constrained controlled optimization problems with application in Lagrange-Hamilton dynamics. Concretely, we formulate and prove necessary conditions of optimality for the considered class of control problems driven by multiple integral cost functionals involving second-order partial derivatives. Moreover, an illustrative example is provided to highlight the effectiveness of the results derived in the paper. In the final part of the paper, we present an algorithm to summarize the steps for solving a control problem such as the one investigated here.