On the Bellman Equation for the Minimum Time Problem in Infinite Dimensions

DOI10.1137/S0363012902419011zbMath1095.49023OpenAlexW2038021629MaRDI QIDQ4652547

Ovidiu Cârjǎ, Piermarco Cannarsa

Publication date: 28 February 2005

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

Full work available at URL: https://doi.org/10.1137/s0363012902419011

zbMATH Keywords

Hamilton-Jacobi-Bellman equationviscosity solutiontime optimal controlinfinite dimensional systemsemilinear parabolic PDE

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Dynamic programming in optimal control and differential games (49L20) Control/observation systems governed by partial differential equations (93C20) Nonlinear systems in control theory (93C10) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

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Proximal analysis and the minimal time function of a class of semilinear control systems ⋮ Time optimal controls of the Cahn-Hilliard equation with internal control ⋮ On the Regularity of the State Constrained Minimal Time Function ⋮ A dual dynamic programming for multidimensional parabolic optimal control problems ⋮ Lower semi-continuity of the solution set for semilinear differential inclusions ⋮ Time optimal controls of the Fitzhugh-Nagumo equation with internal control ⋮ A dual dynamic programming for minimax optimal control problems governed by parabolic equation ⋮ Time optimal controls of the Lengyel-Epstein model with internal control ⋮ Lyapunov pairs for multi-valued semi-linear evolutions ⋮ On the minimum time function and the minimum energy problem; a nonlinear case ⋮ Characterization of Lyapunov pairs in the nonlinear case and applications ⋮ The Bang-bang principle of time optimal controls for the Kuramoto-Sivashinsky-KdV equation with internal control ⋮ A Neumann Boundary Control for Multidimensional Parabolic “Minmax” Control Problems ⋮ Switching Properties of Time Optimal Controls for Systems of Heat Equations Coupled by Constant Matrices

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