Learning-Based Event-Triggered MPC With Gaussian Processes Under Terminal Constraints

The event-triggered control strategy is capable of significantly reducing the number of control task executions while achieving desired control objectives, such as stability. In this article, we introduce a novel learning-based method for event-triggered model predictive control with initially unknown dynamics. The formulation of optimal control problems (OCPs) is based on predictive states derived from Gaussian process (GP) regression under terminal constraints. The event-triggered condition proposed in this article is derived from the recursive feasibility, so that the OCPs are solved only when an error between the predictive and the actual states exceeds a certain threshold. This article analyzes the convergence of the closed-loop system under the event-triggered condition, demonstrating that the system's state will enter the terminal set within a finite time, assuming small-enough uncertainty in the GP model. We validate this approach through a tracking control problem, illustrating its practical effectiveness.