Anytime Ellipsoidal Over-approximation of Forward Reach Sets of Uncertain Linear Systems

TL;DR

This paper introduces an anytime algorithm for computing ellipsoidal over-approximations of reach sets in uncertain linear systems, enabling dynamic accuracy adjustments based on available computational resources while ensuring safety.

Contribution

It presents a novel anytime approach for ellipsoidal over-approximation of reach sets, adaptable to varying computational resources in safety-critical systems.

Findings

The algorithm guarantees safe over-approximations regardless of computation time.

It allows dynamic trade-offs between approximation accuracy and computational effort.

Numerical example demonstrates effectiveness and adaptability of the method.

Abstract

Computing tight over-approximation of reach sets of a controlled uncertain dynamical system is a common practice in verification of safety-critical cyber-physical systems (CPS). While several algorithms are available for this purpose, they tend to be computationally demanding in CPS applications since here, the computational resources such as processor availability tend to be scarce, time-varying and difficult to model. A natural idea then is to design "computation-aware" algorithms that can dynamically adapt with respect to the processor availability in a provably safe manner. Even though this idea should be applicable in broader context, here we focus on ellipsoidal over-approximations. We demonstrate that the algorithms for ellipsoidal over-approximation of reach sets of uncertain linear systems, are well-suited for anytime implementation in the sense the quality of the over-approximation can be dynamically traded off depending on the computational time available, all the while guaranteeing safety. We give a numerical example to illustrate the idea, and point out possible future directions.