Efficient Representation and Computation of Reachable Sets for Hybrid Systems

Abstract

Abstract. Computing reachable sets is an essential step in most analysis and synthesis techniques for hybrid systems. The representation of these sets has a deciding impact on the computational complexity and thus the applicability of these techniques. This paper presents a new approach for approximating reachable sets using oriented rectangular hulls (ORHs), the orientations of which are determined by singular value decompositions of sample covariance matrices for sets of reachable states. The orientations keep the over-approximation of the reachable sets small in most cases with a complexity of low polynomial order with respect to the dimension of the continuous state space. We show how the use of ORHs can improve the efficiency of reachable set computation significantly for hybrid systems with nonlinear continuous dynamics.

PHAVer: Algorithmic Verification of Hybrid Systems Past HyTech

“…Our on-the-fly overapproximation essentially performs a partitioning of the state space similar to the approach in [14]. For the simplification of polyhedra it has been suggested to use bounding boxes or oriented rectangular hulls [15]. Instead, we propose to simply drop the least significant of the constraints, as this seems a good compromise in terms of accuracy and speed.…”

Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis

“…Reachability analysis has been a major research issue in hybrid systems over the past decade [1][2][3][4][5][6][7][8][9]. This research has been motivated by the fact that a successful reachability analysis makes it possible to extend approaches, initially developed in the field of computer science for discrete systems, for analysis and control of hybrid systems [10][11][12][13].…”

“…The next step was to improve the scalability of these approaches in order to be able to handle larger hybrid systems. Various scalable approaches have been proposed for the reachability analysis of continuous (essentially linear) systems based on classes of polytopes such as hyper-rectangles [6] and zonotopes [7,8], or on ellipsoids [9]. However, in order to use these techniques for the analysis of hybrid systems, we must also deal with the discrete transitions in a satisfactory (i.e.…”

Trajectory Based Verification Using Local Finite-Time Invariance

“…Understanding the importance of the problem, the hybrid systems community has put a lot of efforts in the research of reachability analysis and verification. We refer the reader to [7,8,9,10,11,12,13,14,15,16] for some of the earlier references in this topic 1 .…”