Second order optimality conditions in a new Lagrangian formulation for optimal control problems

TL;DR

This paper extends the Lagrangian formulation of optimal control problems with second order dynamics to include second order necessary optimality conditions, providing a complete variational characterization.

Contribution

It introduces second order optimality conditions within a new Lagrangian framework for second order dynamical systems in optimal control.

Findings

Derived second order necessary optimality conditions

Provided a complete characterization of optimality conditions

Extended previous first order results to second order

Abstract

It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on the variational approach. In this paper we extend the first order necessary optimality conditions obtained previously to second order optimality conditions. This results in a complete characterization of the optimality conditions in a new Lagrangian form.