A new Lagrangian approach to optimal control of second-order systems

Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Sato Martin de Almagro R (2025)

Publication Type: Journal article, Original article

Publication year: 2025

Journal

Nonlinearity Institute of Physics: Hybrid Open Access

Book Volume: 38

Article Number: 11

DOI: 10.1088/1361-6544/ae1d08

Abstract

In this work, we propose and study a new approach to formulate the optimal control problem of second-order differential equations, with a particular interest in those derived from force-controlled Lagrangian systems. The formulation results in a new hyperregular control Lagrangian and, thus, a new control Hamiltonian whose equations of motion provide necessary optimality conditions. We compare this approach to the weak Pontryagin’s maximum principle (PMP) in this setting, providing geometric insight into their relation. This leads us to define an extended Tulczyjew’s triple with controls. Moreover, we study the relationship between Noether symmetries of this new formulation and those of the PMP.

Authors with CRIS profile

Michael Konopik Institute of Applied Dynamics Sigrid Leyendecker Institute of Applied Dynamics Rodrigo Sato Martin de Almagro Institute of Applied Dynamics

Involved external institutions

Universität Paderborn DE Germany (DE)

How to cite

APA:

Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., & Sato Martin de Almagro, R. (2025). A new Lagrangian approach to optimal control of second-order systems. Nonlinearity, 38. https://doi.org/10.1088/1361-6544/ae1d08

MLA:

Konopik, Michael, et al. "A new Lagrangian approach to optimal control of second-order systems." Nonlinearity 38 (2025).

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