Optimal control, contact dynamics and Herglotz variational problem

2020/06/25 by Manuel de León, de León, Manuel, Manuel Laínz +3 · 3 citations
Computer Science · Engineering · #37J55 (Primary) 80M50 #49J15 #70Q05 (Secondary) #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities #Control and Stability of Dynamical Systems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2006.14326

openalex publication_date 2020/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin Maximum Principle. As an important result, among others, we develop a contact Pontryagin Maximum Principle that permits to deal with optimal control problems with dissipation. We also consider the Herglotz optimal control problem, which is simultaneously a generalization of the Herglotz variational principle and an optimal control problem. An application to the study of a thermodynamic system is provided.

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• Structure-Preserving Optimal Control of Open Quantum Systems via a Discrete Contact PMP
• From variational principles to geometry
• Herglotz's formalism, Eisenhart lift and Killing vectors

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