Tight Continuous-Time Reachtubes for Lagrangian Reachability

TL;DR

This paper presents CLRT, a novel algorithm for computing tight, continuous-time reachtubes of nonlinear dynamical systems using strain theory and optimization, outperforming existing tools like CAPD.

Contribution

Introduction of CLRT, a new method employing explicit formulas and strain theory for tighter, continuous reachtubes in nonlinear systems, improving over prior semi-definite programming approaches.

Findings

CLRT produces tighter reachtubes than CAPD.

CLRT's formulas simplify and accelerate reachtube computation.

Benchmark results show CLRT's superior performance.

Abstract

We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight and continuous-time reachtube for the solution flows of a nonlinear, time-variant dynamical system. CLRT employs finite strain theory to determine the deformation of the solution set from time $t_i$ to time $t_{i+1}$. We have developed simple explicit analytic formulas for the optimal metric for this deformation; this is superior to prior work, which used semi-definite programming. CLRT also uses infinitesimal strain theory to derive an optimal time increment $h_i$ between $t_i$ and $t_{i+1}$, nonlinear optimization to minimally bloat (i.e., using a minimal radius) the state set at time $t_i$ such that it includes all the states of the solution flow in the interval $[t_i,t_{i+1}]$. We use $\delta$-satisfiability to ensure the correctness of the bloating. Our results on a series of benchmarks show that CLRT performs favorably compared to state-of-the-art tools such as CAPD in terms of the continuous reachtube volumes they compute.