Context-dependent Runtime Construction of Safe Regions of Attraction from Design-Time Identification for Multi-Candidate Simplex Architectures

Overview & Synopsis

Deploying safety-critical cyber-physical systems requires control strategies that reconcile high performance and adaptability with rigorous safety guarantees. Classical control strategies offer stability proofs but are conservative, while advanced optimization- and learning-based controllers achieve high performance but lack formal verification. Runtime Assurance (RTA) architectures bridge this gap by introducing their own (dis-)advantages. Safety filters use online optimization and introduce chattering, while Simplex permissiveness is bounded by the tightness of the certified Region of Attraction (RoA) of its High-Assurance (HA) controller. Targeting this conservatism, we present a two-stage RoA certification procedure leveraging contraction-based stability to establish a target set for Taylor-model-based reachability analysis. We then treat the closed-loop system under HA control as a switched system, enabling: (a) runtime construction of context-dependent safe RoA and (b) safe switching between HA candidates to optimize recovery and maximize the operating envelope of the uncertified High-Performance (HP) controller. We validate this framework on a robotic path-tracking task using a three-stage evaluation: Ordinary Differential Equation (ODE) simulation for theoretical verification, high-fidelity Gazebo simulation under unmodeled dynamics, and experiments on physical hardware. Results show that the Simplex architecture maintains safety under fault injection and successfully shields a behavioral-cloning-trained HP controller. Crucially, the decision module introduces negligible overhead (0.028 ms average, 4.13 ms worst-case), consuming under 10 % of the control period.