Filippov's and Filippov-Ważewski's theorems on closed domains

DOI10.1006/jdeq.2000.3711zbMath0956.34012OpenAlexW1994996557MaRDI QIDQ1975462

Hélène Frankowska, Franco Rampazzo

Publication date: 28 August 2000

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3711

zbMATH Keywords

optimal controlstate constraintsdifferential inclusionsCauchy problemsvalue functionsexistence of neighbouring trajectories relaxation

Mathematics Subject Classification ID

Related Items (37)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A boundary-value problem for Hamilton-Jacobi equations in Hilbert spaces
• Continuity of admissible trajectories for state constraints control problems
• Multivalued dynamics on a closed domain with absorbing boundary. Applications to optimal control problems with integral constraints
• Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. II. Equations of control problems with state constraints
• On nonconvex differential inclusions whose state is constrained in the closure of an open set. Applications to dynamic programming
• Hamilton-Jacobi Equations with State Constraints
• Optimal Control with State-Space Constraint I
• Viscosity Solutions of Hamilton-Jacobi Equations
• Clarke's tangent cones and the boundaries of closed sets in Rn
• Relaxation of Control Systems Under State Constraints
• Some Properties of Constrained Viscosity Solutions of Hamilton–Jacobi–Bellman Equations
• On Nonlinear Optimal Control Problems with State Constraints
• A New Formulation of State Constraint Problems for First-Order PDEs
• Set-valued analysis

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