Safe Control of Feedback-Interconnected Systems via Singular Perturbations
This work addresses safety-critical control for complex systems like robotics and optimization algorithms, but it is incremental as it builds on existing Control Barrier Functions and singular perturbation techniques.
The paper tackles the problem of ensuring safety in feedback-interconnected systems with different timescales by developing a method to extend safety certificates from reduced-order models to the full system, demonstrating its effectiveness in numerical tests on a robotic arm and an optimization-driven plant.
Control Barrier Functions (CBFs) have emerged as a powerful tool in the design of safety-critical controllers for nonlinear systems. In modern applications, complex systems often involve the feedback interconnection of subsystems evolving at different timescales, e.g., two parts from different physical domains (e.g., the electrical and mechanical parts of robotic systems) or a physical plant and an (optimization or control) algorithm. In these scenarios, safety constraints often involve only a portion of the overall system. Inspired by singular perturbations for stability analysis, we develop a formal procedure to lift a safety certificate designed on a reduced-order model to the overall feedback-interconnected system. Specifically, we show that under a sufficient timescale separation between slow and fast dynamics, a composite CBF can be designed to certify the forward invariance of the safe set for the interconnected system. As a result, the online safety filter only needs to be solved for the lower-dimensional, reduced-order model. We numerically test the proposed approach on: (i) a robotic arm with joint motor dynamics, and (ii) a physical plant driven by an optimization algorithm.