Moving constraints as stabilizing controls in classical mechanics

DOI10.1007/s00205-009-0237-6zbMath1304.70028arXiv0804.0398OpenAlexW3101032429WikidataQ59263946 ScholiaQ59263946MaRDI QIDQ982280

Franco Rampazzo, Alberto Bressan

Publication date: 6 July 2010

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.0398

Mathematics Subject Classification ID

Control of mechanical systems (70Q05) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lagrange's equations (70H03)

Related Items

GOH Conditions for Minima of Nonsmooth Problems with Unbounded Controls, Lack of BV bounds for impulsive control systems, Singular Limits for Impulsive Lagrangian Systems with Dissipative Sources, Discontinuous solutions in the optimal control problems and their representation by singular space-time transformations, On BV-extension of asymptotically constrained control-affine systems and complementarity problem for measure differential equations, On \(\mathcal L^1\) limit solutions in impulsive control, Normality and gap phenomena in optimal unbounded control, Metric geometry of nonregular weighted Carnot-Carathéodory spaces, \(\mathcal{L}^1\) limit solutions for control systems, Stabilizability in optimal control, Graph completions for impulsive feedback controls, Stabilizability in optimization problems with unbounded data, A Higher-Order Maximum Principle for Impulsive Optimal Control Problems, Converse Lyapunov theorems for control systems with unbounded controls, Nondegenerate Abnormality, Controllability, and Gap Phenomena in Optimal Control with State Constraints, Optimal control of dynamical systems with polynomial impulses

Cites Work

• Impulsive control of Lagrangian systems and locomotion in fluids
• On the gap between deterministic and stochastic ordinary differential equations
• Impulsive control systems with commutative vector fields
• Geometry and physics of averaging with applications
• 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.
• Foliated manifolds with bundle-like metrics
• Hamilton-Jacobi-Bellman equations with fast gradient-dependence
• Controlled Lagrangians and the stabilization of Euler-Poincaré mechanical systems
• On Differential Systems with Quadratic Impulses and Their Applications to Lagrangian Mechanics
• Averaging and Vibrational Control of Mechanical Systems
• GEOMETRY OF VIBRATIONAL STABILIZATION AND SOME APPLICATIONS
• Geodesics on vibrating surfaces and curvature of the normal family
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item