Data-Driven Nonconvex Reachability Analysis using Exact Multiplication
This paper addresses a fundamental challenge in data-driven reachability analysis: accurately representing and propagating non-convex reachable sets. We propose a novel approach using constrained polynomial zonotopes to describe reachable sets for unknown LTI systems. Unlike constrained zonotopes commonly used in existing literature, constrained polynomial zonotopes are closed under multiplication with constrained matrix zonotopes. We leverage this property to develop an exact multiplication method that preserves the non-convex geometry of reachable sets without resorting to approximations. We demonstrate that our approach provides tighter over-approximations of reachable sets for LTI systems compared to conventional methods.
Code (1)
Similar Papers 제목 키워드 기반
Data-Driven Reachability with Scenario Optimization and the Holdout Method
Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, hi…
Reachability Analysis Using Constrained Polynomial Logical Zonotopes
In this paper, we propose reachability analysis using constrained polynomial logical zonotopes. We perform reachability analysis to compute the set of states that could be reached. To do this, we utilize a recently intro…
Computational EfficiencyHybrid zonotopes: a new set representation for reachability analysis of mixed logical dynamical systems
This article presents a new set representation named the hybrid zonotope that is equivalent to the union of $2^N$ constrained zonotopes -- convex polytopes -- through the addition of $N$ binary zonotope factors. The majo…
Data-Driven Reachability Analysis Using Matrix Zonotopes
In this paper, we propose a data-driven reachability analysis approach for unknown system dynamics. Reachability analysis is an essential tool for guaranteeing safety properties. However, most current reachability analys…
Efficient Backward Reachability Using the Minkowski Difference of Constrained Zonotopes
Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This paper is concerned with developing scalable algorithms that under-approximate the backward …