Nonconservative Noether's Theorem in Optimal Control
Gastao S. F. Frederico, Delfim F. M. Torres
TL;DR
This paper extends Noether's theorem to optimal control systems influenced by nonconservative forces, providing a systematic method to derive conservation laws and connecting previous results in mechanics and calculus of variations.
Contribution
It introduces a generalized Noether's theorem for nonconservative optimal control systems, offering a systematic approach to find conservation laws.
Findings
Derived conservation laws for nonconservative optimal control problems
Unified previous results in mechanics and calculus of variations
Provided a systematic method for calculating conservation laws
Abstract
We extend Noether's theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the conserved quantities previously obtained in the literature for nonconservative problems of mechanics and the calculus of variations are derived.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Quantum chaos and dynamical systems · Nonlinear Waves and Solitons