TTT: A Temporal Refinement Heuristic for Tenuously Tractable Discrete Time Reachability Problems

TL;DR

This paper proposes a temporal refinement heuristic for reachability analysis of complex control systems, balancing computational efficiency and accuracy by adaptively choosing when to perform detailed symbolic versus faster concrete queries.

Contribution

It introduces a novel temporal refinement algorithm that improves the efficiency of reachable set computation for nonlinear systems with neural controllers.

Findings

Achieves 20-70% reduction in computation time compared to baseline methods.

Maintains similar approximation error levels with less computational effort.

Demonstrates effectiveness on systems with neural network controllers.

Abstract

Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for complex control systems, e.g., with nonlinear dynamics and/or a neural network controller, is often either slow or overly conservative. To address these challenges, much literature has focused on spatial refinement, i.e., tuning the discretization of the input sets and intermediate reachable sets. This paper introduces the idea of temporal refinement: automatically choosing when along the horizon of the reachability problem to execute slow symbolic queries which incur less approximation error versus fast concrete queries which incur more approximation error. Temporal refinement can be combined with other refinement approaches as an additional tool to trade off tractability and tightness in approximate reachable set computation. We introduce a temporal refinement algorithm and demonstrate its effectiveness at computing approximate reachable sets for nonlinear systems with neural network controllers. We calculate reachable sets with varying computational budget and show that our algorithm can generate approximate reachable sets with a similar amount of error to the baseline in 20-70% less time.