Optimal control of underactuated mechanical systems: A geometric approach

DOI10.1063/1.3456158zbMath1312.70008arXiv0912.2033OpenAlexW3099452328MaRDI QIDQ5253728

David Martín de Diego, Leonardo Colombo, Marcela Zuccalli

Publication date: 27 May 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.2033

Mathematics Subject Classification ID

Control of mechanical systems (70Q05) Optimality conditions for problems involving ordinary differential equations (49K15) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Lagrange's equations (70H03)

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Cites Work

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• Geometric control and numerical aspects of nonholonomic systems
• Geometric approach to Pontryagin's maximum principle
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Nonholonomic mechanics and control. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden. With scientific input from P. S. Krishnaprasad, R. M. Murray, and D. Zenkov.
• Variational principles for constrained systems: Theory and experiment
• Discrete mechanics and optimal control: An analysis
• Generalized Hamiltonian dynamics. I. Formulation on T*Q⊕T Q
• Discrete mechanics and variational integrators
• Discrete vakonomic mechanics
• Higher-order differential equations and higher-order lagrangian mechanics
• Control problems in super-articulated mechanical systems
• Geometric Description of Vakonomic and Nonholonomic Dynamics. Comparison of Solutions
• Skinner–Rusk unified formalism for optimal control systems and applications
• HIGHER-ORDER DISCRETE LAGRANGIAN MECHANICS

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