Towards optimal space-time discretization for reachable sets of nonlinear control systems

2023/05/22 by Janosch Rieger, Rieger, Janosch, Kyria Wawryk +1
Engineering · Mathematics · #65L50 #93B03 #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #Control Systems and Identification #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2305.12727

openalex publication_date 2023/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial discretizations of Euler's method for reachable set computation in a non-uniform way to improve the performance of the method.

Related

• Efficient space-time discretizations for tracking the boundaries of reachable sets
• TTT: A Temporal Refinement Heuristic for Tenuously Tractable Discrete Time Reachability Problems
• Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 2: Numerical Computations
• Approximation of reachable sets using optimal control and support vector machines
• A linear programming approach to approximating the infinite time reachable set of strictly stable linear control systems