A linear programming approach to approximating the infinite time reachable set of strictly stable linear control systems

2019/02/14 by Andreas Ernst, Ernst, Andreas, Lars Grüne +3
Computer Science · Engineering · #90C05 #93B03 #93D20 #Advanced Control Systems Optimization #FOS: Mathematics #Formal Methods in Verification #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.1902.05239

openalex publication_date 2019/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with fixed facet normals as an outer approximation of the limit set. In particular, this approach does not rely on forward iteration of finite-time reachable sets.

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