A NEW LAGRANGIAN APPROACH TO CONTROL AFFINE SYSTEMS WITH A QUADRATIC LAGRANGE TERM
Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Sato Martin de Almagro R, Szemenyei F (2024)
Publication Type: Journal article
Publication year: 2024
Journal
Book Volume: 11
Pages Range: 336-353
Journal Issue: 3
DOI: 10.3934/jcd.2024017
Abstract
In this work, we consider optimal control problems for mechanical systems with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term. Classically, Pontryagin’s maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way.
Authors with CRIS profile
Sigrid Leyendecker
Institute of Applied Dynamics
Rodrigo Sato Martin de Almagro
Institute of Applied Dynamics
Flóra Szemenyei
Institute of Applied Dynamics
Involved external institutions
Germany (DE)How to cite
APA:
Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Sato Martin de Almagro, R., & Szemenyei, F. (2024). A NEW LAGRANGIAN APPROACH TO CONTROL AFFINE SYSTEMS WITH A QUADRATIC LAGRANGE TERM. Journal of Computational Dynamics, 11(3), 336-353. https://doi.org/10.3934/jcd.2024017
MLA:
Leyendecker, Sigrid, et al. "A NEW LAGRANGIAN APPROACH TO CONTROL AFFINE SYSTEMS WITH A QUADRATIC LAGRANGE TERM." Journal of Computational Dynamics 11.3 (2024): 336-353.
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