Geometric reduction in optimal control theory with symmetries

DOI10.1016/S0034-4877(03)90006-1zbMath1051.49011arXivmath-ph/0206036OpenAlexW3104319045WikidataQ57948234 ScholiaQ57948234MaRDI QIDQ1422465

Jesús Marín-Solano, Arturo Echeverría-Enríquez, Miguel C. Muñoz-Lecanda, Narciso Román-Roy

Publication date: 15 February 2004

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0206036

zbMATH Keywords

optimal controlsymmetriesPontryagin maximum principleMarsden-Weinstein reduction theorempresymplectic Hamiltonian systems

Mathematics Subject Classification ID

Related Items (12)

Remarks on multisymplectic reduction ⋮ A different look at the optimal control of the Brockett integrator ⋮ Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups ⋮ Optimal reduction of controlled Hamiltonian system with Poisson structure and symmetry ⋮ Lie-Poisson reduction for optimal control of left-invariant control systems with subgroup symmetry ⋮ Geometric methods for adjoint systems ⋮ On symmetries in time optimal control, sub-Riemannian geometries, and the \(K-P\) problem ⋮ General symmetries in optimal control ⋮ Singular reduction for nonlinear control systems ⋮ Geometric approach to Pontryagin's maximum principle ⋮ CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS ⋮ Optimal control, contact dynamics and Herglotz variational problem

Cites Work

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• Reduction of symplectic manifolds with symmetry
• Nonlinear control systems.
• Some geometric aspects of variational calculus in constrained systems
• Fibre derivatives: Some applications to singular Lagrangians
• Nonlinearizable single-input control systems do not admit stationary symmetries
• Reduction of constrained mechanical systems and stability of relative equilibria
• The Hamilton-Cartan formalism in the calculus of variations
• Optimal control and implicit Hamiltonian systems
• Presymplectic manifolds and the Dirac–Bergmann theory of constraints
• REDUCTION OF PRESYMPLECTIC MANIFOLDS WITH SYMMETRY
• Symmetries in Optimal Control
• Lie Theory and Control Systems Defined on Spheres
• System Theory on Group Manifolds and Coset Spaces
• Symmetry and reduction in implicit generalized Hamiltonian systems
• Symmetries in vakonomic dynamics: Applications to optimal control
• Time-dependent Lagrangians invariant by a vector field

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