Constrained controlled optimization problems involving second-order derivatives

Abstract

In this paper, we investigate the nonlinear Lagrange dynamics associated with two classes of constrained controlled optimization problems involving second- order derivatives. More precisely, we formulate and prove necessary conditions of optimality for the considered variational control problems governed by simple integral functionals and second-order ordinary differential equation (ODE)/ isoperimetric constraints. Moreover, we propose an algorithm to synthesize the concrete steps to be followed for solving constrained controlled optimization problems.

Mathematics Subject Classification (2020):

• 49K15
• 49K20
• 49K21
• 65K10

Key words:

• Controlled second-order Lagrangian
• Euler-Lagrange equations
• isoperimetric constraints
• simple integral functional