Asymptotic Controllability and Lyapunov-like Functions Determined by Lie Brackets

DOI10.1137/16M1086947zbMath1401.93039arXiv1608.02712WikidataQ129904653 ScholiaQ129904653MaRDI QIDQ4636348

Monica Motta, Franco Rampazzo

Publication date: 19 April 2018

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.02712

zbMATH Keywords

Lyapunov functionsLie bracketspartial differential inequalitiesglobal asymptotic controllability

Mathematics Subject Classification ID

Controllability (93B05) Control/observation systems governed by partial differential equations (93C20) Stabilization of systems by feedback (93D15) Lyapunov and storage functions (93D30)

Related Items

HJ inequalities involving Lie brackets and feedback stabilizability with cost regulation, A Hamiltonian approach to small time local attainability of manifolds for nonlinear control systems, Robust feedback stabilization by means of Lyapunov-like functions determined by Lie brackets, A degenerate elliptic equation for second order controllability of nonlinear systems, The Aronsson equation, Lyapunov functions, and local Lipschitz regularity of the minimum time function

Cites Work

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• Integral representations for bracket-generating multi-flows
• New results on sampled-data feedback stabilization for autonomous nonlinear systems
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Commutators of flow maps of nonsmooth vector fields
• Higher order necessary conditions in optimal control theory
• Hölder continuity of the minimum-time function for \(C^ 1\)-manifold targets
• Iterated Lie brackets for nonsmooth vector fields
• Control theory from the geometric viewpoint.
• Asymptotic controllability and optimal control
• A geometric approach to feedback stabilization of nonlinear systems with drift
• Existence of Lipschitz and Semiconcave Control-Lyapunov Functions
• Sufficient Lie Algebraic Conditions for Sampled-Data Feedback Stabilizability of Affine in the Control Nonlinear Systems
• A Lyapunov-Like Characterization of Asymptotic Controllability
• Patchy Vector Fields and Asymptotic Stabilization
• Local small time controllability and attainability of a set for nonlinear control system
• Asymptotic controllability implies feedback stabilization
• Feedback Stabilization and Lyapunov Functions
• Global Asymptotic Controllability Implies Input-to-State Stabilization
• Controllability of Some Nonlinear Systems with Drift via Generalized Curvature Properties
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
• Liapunov functions and stability in control theory