Adaptive parameter tuning for reachability analysis of nonlinear systems

Abstract

Reachability analysis fails to produce tight reachable sets if certain algorithm parameters are poorly tuned, such as the time step size or the accuracy of the set representation. The tuning is especially difficult in the context of nonlinear systems where over-approximation errors accumulate over time due to the so-called wrapping effect, often requiring expert knowledge. In order to widen the applicability of reachability analysis for practitioners, we propose the first adaptive parameter tuning approach for reachability analysis of nonlinear continuous systems tuning all algorithm parameters. Our modular approach can be applied to different reachability algorithms as well as various set representations. Finally, an evaluation on numerous benchmark systems shows that the adaptive parameter tuning approach efficiently computes very tight enclosures of reachable sets. CCS CONCEPTS• General and reference → Verification; • Mathematics of computing → Ordinary differential equations.

RINO: Robust INner and Outer Approximated Reachability of Neural Networks Controlled Systems

“…The precision is relatively stable and does not necessarily improve when decreasing the time step. Indeed, as already noted [25], the improvement in approximation by Taylor models on smaller time steps is balanced by the loss of precision due to set-based abstraction being performed more often. Note also that the analysis time does not depend linearly on the time step: the control step, which rules the frequency at which the analysis of the neural net controller has to be performed, is fixed (see Table 1) and does not depend on the integration time step.…”

Provably Safe Reinforcement Learning via Action Projection Using Reachability Analysis and Polynomial Zonotopes

“…Since the settings for reachability analysis can be tuned automatically [60], [61], the main design parameters for our safety shield in addition to the type of control law discussed in Sec. V-A are the planning horizon t f and the replanning time t c .…”

Adaptive reachability algorithms for nonlinear systems using abstraction error analysis

“…Essentially, two types of approaches exist: The majority of methods computes an over-approximation that is as tight as possible for a desired (lower) user-specified order. The alternative approach in [30,Thm. 3.2] reduces the or-der as much as possible for a given bound of the induced over-approximation.…”

“…Another method [45] proposes iterative recomputations of the reachable set from scratch, while refining the parameter values in discrete steps in between runs. The work in [30] presents the first fully automatic reachability algorithm for nonlinear systems, which not only optimizes the time step size, but also other algorithm parameters such as the representation size.…”