Safety-Critical Control of Multi-Timescale Nonlinear Systems

Abstract

Guaranteeing safety in control systems has become increasingly important in recent years. This paper addresses the problem of safe trajectory tracking control for nonlinear multi-timescale systems modeled as singularly perturbed systems with slow and fast subsystems. We propose a real-time control framework consisting of two hierarchical layers, where the first layer ensures tracking and safety for the reduced-order slow subsystem, while the second layer enforces safety and stability for the fast subsystem. Each layer incorporates a Control Lyapunov Function (CLF) to ensure stability and tracking, and Control Barrier Functions (CBFs) to enforce safety constraints. The CLF and CBF conditions are unified and solved at each layer through a real-time optimization problem. A composite Lyapunov approach is employed to ensure overall tracking performance. We further prove that the overall safety of the system is guaranteed when both subsystems satisfy their respective safety constraints. Simulation results on a planar quadrotor performing obstacle avoidance and trajectory tracking demonstrate the effectiveness of the proposed method for nonlinear multi-timescale systems.