Runtime Assurance With Stability Regulation

Runtime assurance refers to a supervisory method in control of dynamical systems. In the existing literature, it is used to monitor the behavior of a dynamical system for potential failures or violations of predefined trajectory boundaries. Under nominal conditions, the use of a complex or nondeterministic control law is allowed, where this law is switched to a safe one when such violations are detected. In this paper, we introduce a novel runtime assurance approach that diverges from methods found in the existing literature. Specifically, a general runtime assurance with a stability regulation framework is proposed. A complex or nondeterministic control law is permitted to drive the dynamical system when a predefined stability metric is met, and otherwise, a safe control law, inherently satisfying this metric, takes over. The key feature of the proposed framework is its flexibility in selecting the stability metric, which can be based on Lyapunov stability, asymptotic stability, exponential stability, or boundedness of system trajectories. Illustrative numerical examples are also provided to demonstrate the efficacy of the proposed framework.