Lipschitz continuity of the value function in optimal control

DOI10.1023/A:1022683628650zbMath0901.49022OpenAlexW1565973198WikidataQ58296892 ScholiaQ58296892MaRDI QIDQ1367721

Vladimir M. Veliov

Publication date: 27 May 1998

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1022683628650

zbMATH Keywords

discretizationLipschitz continuityvalue functionviabilityoptimal control theoryminimum-time problems

Mathematics Subject Classification ID

Related Items (19)

On open-loop and feedback attainability of a closed set for nonlinear control systems ⋮ Regularity of the minimum time and of viscosity solutions of degenerate eikonal equations via generalized Lie brackets ⋮ Convexity properties of the minimum time function ⋮ On the Regularity of the State Constrained Minimal Time Function ⋮ Asymptotic solutions of Hamilton-Jacobi equations with state constraints ⋮ Existence of solutions to a global eikonal equation ⋮ On the continuity of optimal controls and value functions with respect to initial conditions ⋮ Lipschitz regularity of the minimum time function of differential inclusions with state constraints ⋮ Kinodynamic Control Systems and Discontinuities in Clearance ⋮ Local small time controllability and attainability of a set for nonlinear control system ⋮ Lipschitz continuity and local semiconcavity for exit time problems with state constraints ⋮ Continuous dependence of optimal control to controlled domain of actuator for heat equation ⋮ Sufficient Conditions for Small Time Local Attainability for a Class of Control Systems ⋮ The state constrained bilateral minimal time function ⋮ Variational Analysis and Regularity of the Minimum Time Function for Differential Inclusions ⋮ Differential games with incomplete information and with signal revealing: the symmetric case ⋮ Semigeodesics and the minimal time function ⋮ Interior sphere property of attainable sets and time optimal control problems ⋮ Controllability of Some Nonlinear Systems with Drift via Generalized Curvature Properties

Cites Work

• Self-accessibility of a set with respect to a multivalued field
• Error estimates for discretized differential inclusions
• Second order discrete approximations to strongly convex differential inclusions
• Hölder continuity of the minimum-time function for \(C^ 1\)-manifold targets
• Convexity properties of the minimum time function
• Qualitative properties of trajectories of control systems: a survey
• An Approximation Scheme for the Minimum Time Function
• Optimization and nonsmooth analysis
• A General Theorem on Local Controllability
• Second-Order Discrete Approximation to Linear Differential Inclusions
• Optimal Feedback Controls
• Hamilton–Jacobi Theory for Optimal Control Problems with Data Measurable in Time
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