Approximation of reachable sets by direct solution methods for optimal control problems

DOI10.1080/10556780600604999zbMath1129.93003OpenAlexW2024730047MaRDI QIDQ5436912

Robert Baier, Ilyes Aïssa Chahma, Matthias Gerdts, Christof Büskens

Publication date: 18 January 2008

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://epub.uni-bayreuth.de/5542/1/baier_chahma_gerdts_et_al_opt_meth_softw_2007.pdf

zbMATH Keywords

order of convergencedirect solution methodsdiscretization of optimal control problemsapproximation of reachable setsset-valued Runge-Kutta methods

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Attainable sets, reachability (93B03) Discrete approximations in optimal control (49M25) Linear optimal control problems (49N05)

Related Items (8)

A linear programming approach to approximating the infinite time reachable set of strictly stable linear control systems ⋮ A novel unified framework for solving reachability and invariance problems ⋮ Towards optimal space-time discretization for reachable sets of nonlinear control systems ⋮ Estimation of Star-Shaped Reachable Sets of Nonlinear Control Systems ⋮ Approximation of convex bodies by multiple objective optimization and an application in reachable sets ⋮ Approximation of reachable sets using optimal control and support vector machines ⋮ Construction of the minimum time function for linear systems via higher-order set-valued methods ⋮ Reachable set computation of linear systems with nonconvex constraints via convex optimization

Cites Work

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• Differential inclusions and optimal control
• Error estimates for discretized differential inclusions
• Second order discrete approximations to strongly convex differential inclusions
• Approximation of the viability kernel
• Ellipsoidal calculus for estimation and control
• Higher-order approximations of linear control systems via Runge-Kutta schemes
• Comparative properties of three metrics in the space of compact convex sets
• Direct shooting method for the numerical solution of higher-index DAE optimal control problems
• Ellipsoidal techniques for reachability analysis: Internal approximation
• Runge-Kutta methods in optimal control and the transformed adjoint system
• Integrals of set-valued functions
• The Cutting-Plane Method for Solving Convex Programs
• Approximating reachable sets for a class of linear control systems†
• Second-Order Discrete Approximation to Linear Differential Inclusions
• Difference Methods for Differential Inclusions: A Survey
• Second-Order Runge--Kutta Approximations in Control Constrained Optimal Control
• On Ellipsoidal Techniques for Reachability Analysis. Part I: External Approximations
• On Ellipsoidal Techniques for Reachability Analysis. Part II: Internal Approximations Box-valued Constraints
• The Bang-Bang Principle for Linear Control Systems
• State Constraints in Convex Control Problems of Bolza
• Higher order numerical schemes for affinely controlled nonlinear systems

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