Stability and Convergence of Euler's Method for State-Constrained Differential Inclusions

DOI10.1137/060661867zbMath1262.34021OpenAlexW2057039419MaRDI QIDQ3519418

Robert Baier, Ilyes Aïssa Chahma, Frank Lempio

Publication date: 14 August 2008

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

Full work available at URL: https://semanticscholar.org/paper/d392372ad549e2278cb1b89e22f76c975cf82608

zbMATH Keywords

Filippov theoremdifferential inclusions with state constraintsset-valued Euler's methodstability and convergence of discrete approximations

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Ordinary differential inclusions (34A60) Stability and convergence of numerical methods for ordinary differential equations (65L20) Existence theories for optimal control problems involving ordinary differential equations (49J15)

Related Items (16)

Discretizations of Linear Elliptic Partial Differential Inclusions ⋮ On elimination of state constraints in the construction of reachable sets ⋮ The Euler scheme for state constrained ordinary differential inclusions ⋮ On the attainability problem under state constraints with piecewise smooth boundary ⋮ Convergence order of implicit Euler numerical scheme for maximal monotone differential inclusions ⋮ Algorithm of uniform filling of nonlinear dynamic system reachable set based on maximin problem solution ⋮ A Filippov approximation theorem for strengthened one-sided Lipschitz differential inclusions ⋮ Towards optimal space-time discretization for reachable sets of nonlinear control systems ⋮ A differential inclusion approach for modeling and analysis of dynamical systems under uncertainty ⋮ Convergence results for the discrete regularization of linear-quadratic control problems with bang-bang solutions ⋮ Approximations of linear control problems with bang-bang solutions ⋮ An implicit discretization scheme for linear-quadratic control problems with bang–bang solutions ⋮ Optimization-based subdivision algorithm for reachable sets ⋮ Discrete Filippov-Type Stability for One-Sided Lipschitzian Difference Inclusions ⋮ Internal approximations of reachable sets of control systems with state constraints ⋮ On reachability analysis for nonlinear control systems with state constraints

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