A Lyapunov-Based Event-Triggered Model Predictive Control Approach for Safe Tracking Control of Discrete-Time Nonlinear Systems

In this article, a novel Lyapunov-based event-trigger mechanism is proposed to reduce the computation cost of model predictive control (MPC) algorithm for discrete-time nonlinear input-affine safety-critical systems. Unlike conventional approaches that require continuous error monitoring, the proposed mechanism leverages the predictive capability of MPC to determine triggering instants directly based on the evolution of the closed-loop Lyapunov function. Safety and stability are enforced by incorporating control barrier functions (CBFs) and control Lyapunov functions (CLFs) as constraints within the MPC optimization. Furthermore, the recursive feasibility of the proposed event-triggered MPC algorithm is rigorously analyzed, with special attention to the potential infeasibility caused by hard CBF constraints. Input-to-state practical stability (ISpS) of the resulting closed-loop system is also established. Simulation results demonstrate that the proposed event-triggered CBF-CLF-MPC algorithm effectively eliminates unnecessary controller updates, reducing computational consumption while maintaining tracking performance comparable to that of a conventional time-triggered MPC algorithm.