Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions

TL;DR

This paper introduces a novel, efficient set-based method for reachability analysis of parametric linear hybrid systems with time-triggered transitions, significantly reducing computation time and enabling more complex modeling.

Contribution

The paper presents a new approach that decouples time and spatial variables and uses interval matrix maps on zonotopes, achieving up to 5000 times faster computations.

Findings

Achieved 5000x reduction in computation time compared to previous methods.

Successfully applied to an electro-mechanical braking system model.

Enables more expressive hybrid system models with lower computational costs.

Abstract

Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle systems with uncertain parameters and inputs, where the uncertainties are bound to given intervals. The method is evaluated on the plant model of an experimental electro-mechanical braking system with periodic controller. In this model, the fast-switching controller dynamics requires simulation time scales of the order of nanoseconds. Accurate set-based computations for relatively large time horizons are known to be expensive. However, by appropriately decoupling the time variable with respect to the spatial variables, and enclosing the uncertain parameters using interval matrix maps acting on zonotopes, we show that the computation time can be lowered to 5000 times faster with respect to previous works. This is a step forward in formal verification of hybrid systems because reduced run-times allow engineers to introduce more expressiveness in their models with a relatively inexpensive computational cost.