Controlled nonlinear dynamics generated by isoperimetric constrained optimization problems involving second-order partial derivatives

The present paper investigates the nonlinear Lagrange dynamics generated by two classes of isoperimetric constrained controlled optimization problems involving second-order partial derivatives. More precisely, necessary optimality conditions are formulated and proved for the considered variational control problems governed by multiple and path-independent curvilinear integral functionals. Moreover, the theoretical results derived in the paper are accompanied by some illustrative examples. Also, an algorithm is proposed to synthesize the concrete steps to be followed to solve a constrained controlled optimization problem such as those studied in the paper.