Speaker
Description
In this work, we propose a new framework to treat optimal control problems with second order control systems. Such control systems are usually encountered in mechanics in the form of Euler-Lagrange equations with forcing. The new approach is based on a reformulation of the optimal control problem as a regular Lagrangian variational problem. Such a reformulation is possible because of the second order form of the control system. Classical methods of optimal control theory lead to a non regular Hamiltonian formulation of optimality conditions. Applying variational methods to the new Lagrangian setting, we obtain the optimality conditions in a new form. We show equivalence between the new conditions and the classical ones and provide geometrical characterization of the relationships behind the two settings. The proposed framework allows for a deeper understanding of the structure of optimal control problems with second order system constraints and permits the use of variational integrators for the discretization of the optimal control problems preserving the geometrical structure of optimal solutions.
