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

2025/07/08 by Konopik, Michael, Leyendecker, Sigrid, Maslovskaya, Sofya +2
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2507.06024

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.

Citations

• A new Lagrangian approach to optimal control of second-order systems
• Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term

Related

• A new Lagrangian approach to optimal control of second-order systems
• Second-Order Necessary/Sufficient Conditions for Optimal Control Problems in the Absence of Linear Structure
• Controllability and necessary second-order optimality conditions in optimal control problems
• Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term
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