Optimal Control Problems with Symmetry Breaking Cost Functions

DOI10.1137/16M1091654zbMath1428.49005arXiv1701.06973OpenAlexW2579947342MaRDI QIDQ4603024

Leonardo Colombo, Anthony M. Bloch, Tomoki Ohsawa, Rohit Gupta

Publication date: 14 February 2018

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.06973

zbMATH Keywords

optimal controlEuler-Poincaré equationssymmetry reductionLie-Poisson equations

Mathematics Subject Classification ID

Hamilton's equations (70H05) Existence theories for optimal control problems involving ordinary differential equations (49J15) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lagrange's equations (70H03)

Related Items (3)

Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups ⋮ Lie-Poisson reduction for optimal control of left-invariant control systems with subgroup symmetry ⋮ Dynamic interpolation for obstacle avoidance on Riemannian manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Reduction theory for symmetry breaking with applications to nematic systems
• Hamilton-Pontryagin integrators on Lie groups. I: Introduction and structure-preserving properties
• Control theory on Lie groups
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• General symmetries in optimal control
• Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top
• Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products
• Control theory from the geometric viewpoint.
• The Euler-Poincaré equations and double bracket dissipation
• Nonholonomic mechanics and control. With the collaboration of J. Baillieul, P. E Crouch, J. E. Marsden and D. Zenkov. With scientific input from P. S. Krishnaprasad and R. M. Murray
• Lagrangian reduction by stages
• Semidirect Products and Reduction in Mechanics
• Optimal control of systems possessing symmetries
• Optimal Control for Holonomic and Nonholonomic Mechanical Systems with Symmetry and Lagrangian Reduction
• Discrete Euler-Poincaré and Lie-Poisson equations
• Symmetries in Optimal Control
• Symmetry Reduction of Optimal Control Systems and Principal Connections
• Reduction of Sufficient Conditions for Optimal Control Problems With Subgroup Symmetry
• Lie groups beyond an introduction

This page was built for publication: Optimal Control Problems with Symmetry Breaking Cost Functions