Reachability of Linear Time-Invariant Systems via Ellipsoidal Approximations

Abstract

Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, exhibit exponential computational complexity with respect to the state dimension. In this paper, we show that supersolutions and subsolutions of a Hamilton-Jacobi-Bellman equation can be used to generate under- and over-approximating reachable sets for nonlinear systems, and based on this, we develop a scheme for approximating reachable sets of linear time-invariant systems via ellipsoids with polynomial computational complexity.