Computing finite abstractions with robustness margins via local reachable set over-approximation

TL;DR

This paper introduces a local reachable set over-approximation method for computing finite abstractions of nonlinear systems, enhancing robustness and reducing conservativeness in control synthesis.

Contribution

It presents a novel approach that linearizes nonlinear dynamics locally with error tracking to produce tighter, more reliable finite abstractions for robust hybrid control.

Findings

Tighter approximations of reachable sets compared to global methods

Improved robustness margins in control synthesis

Numerical examples demonstrating effectiveness

Abstract

This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical function to provide bounds on the reachable sets of nonlinear systems, which can be conservative and lead to spurious transitions in the abstract systems. This problem is even more pronounced in the presence of imperfect measurements and modelling uncertainties, where control synthesis can easily become infeasible due to added spurious transitions. To mitigate this problem, we propose to compute finite abstractions with robustness margins by over-approximating the local reachable sets of nonlinear systems. We do so by linearizing the nonlinear dynamics into linear affine systems and keeping track of the linearization error. It is shown that this approach provides tighter approximations and several numerical examples are used to illustrate of effectiveness of the proposed methods.