Optimal Control, Contact Dynamics and Herglotz Variational Problem
Manuel de León, Manuel Laínz, Miguel C. Muñoz‐Lecanda
Abstract
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.
Topics & Concepts
Pontryagin's minimum principleOptimal controlHamiltonian (control theory)Maximum principleMathematicsGeneralizationVariational principleHamiltonian mechanicsControl (management)Calculus of variationsApplied mathematicsMathematical optimizationComputer scienceMathematical analysisPhysicsQuantum mechanicsPhase spaceArtificial intelligenceControl and Stability of Dynamical SystemsContact Mechanics and Variational InequalitiesAdvanced Mathematical Modeling in Engineering