Optimization-based subdivision algorithm for reachable sets

DOI10.3934/jcd.2021005zbMath1467.93028OpenAlexW4239127217MaRDI QIDQ2026921

Robert Baier, Matthias Gerdts, Wolfgang F. Riedl

Publication date: 21 May 2021

Published in: Journal of Computational Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jcd.2021005

zbMATH Keywords

optimal controlnonlinear systemsnonlinear optimizationsubdivisionreachable setsdirect discretization

Mathematics Subject Classification ID

Numerical methods based on nonlinear programming (49M37) Nonlinear systems in control theory (93C10) Attainable sets, reachability (93B03) Discrete approximations in optimal control (49M25)

Related Items (2)

Towards optimal space-time discretization for reachable sets of nonlinear control systems ⋮ External ellipsoidal approximations for set evolution equations

Uses Software

• NAG
• Ipopt
• nag
• Matplotlib
• WORHP
• PovRay

Cites Work

• Unnamed Item
• Approximation of reachable sets using optimal control algorithms
• Approximation of reachable sets using optimal control and support vector machines
• On target for Venus -- set oriented computation of energy efficient low thrust trajectories
• A reachable set analysis method for generating near-optimal trajectories of constrained multiphase systems
• A nonsmooth Newton's method for discretized optimal control problems with state and control constraints
• Error estimates for discretized differential inclusions
• Second order discrete approximations to strongly convex differential inclusions
• A subdivision algorithm for the computation of unstable manifolds and global attractors
• Overapproximating reachable sets by Hamilton-Jacobi projections
• Asymptotic behavior of dynamical and control systems under perturbation and discretization
• The implicit Euler scheme for one-sided Lipschitz differential inclusions
• Filippov's and Filippov-Ważewski's theorems on closed domains
• Traffic networks as information systems. A viability approach
• Numerical fixed grid methods for differential inclusions
• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
• Stability in general control systems
• Stability and Convergence of Euler's Method for State-Constrained Differential Inclusions
• The Exponential Formula for the Reachable Set of a Lipschitz Differential Inclusion
• Difference Methods for Differential Inclusions: A Survey
• Variational Analysis
• Stability and Euler Approximation of One-sided Lipschitz Differential Inclusions
• Exploring invariant sets and invariant measures
• Semi-Lagrangian Approximation Schemes for Linear and Hamilton—Jacobi Equations
• The ESA NLP Solver WORHP
• A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games
• Computing Abstractions of Nonlinear Systems
• Geometric Numerical Integration
• Properties of the solution set of a generalized differential equation
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

This page was built for publication: Optimization-based subdivision algorithm for reachable sets