Learning-based Event-triggered MPC with Gaussian processes under terminal constraints

TL;DR

This paper introduces a learning-based event-triggered model predictive control method using Gaussian processes for nonlinear systems with unknown dynamics, reducing control updates while ensuring stability and convergence.

Contribution

It presents a novel approach combining Gaussian process regression with event-triggered MPC under terminal constraints, enhancing efficiency and stability in controlling unknown nonlinear systems.

Findings

Finite-time convergence to the terminal set is achieved as GP uncertainty decreases.

The proposed method reduces control task executions without sacrificing performance.

Demonstrated effectiveness through a tracking control problem.

Abstract

Event-triggered control strategy is capable of significantly reducing the number of control task executions without sacrificing control performance. In this paper, we propose a novel learning-based approach towards an event-triggered model predictive control (MPC) for nonlinear control systems whose dynamics are unknown apriori. In particular, the optimal control problems (OCPs) are formulated based on predictive states learned by Gaussian process (GP) regression under a terminal constraint constructed by a symbolic abstraction. The event-triggered condition proposed in this paper 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. Based on the event-triggered condition, we analyze the stability of the closed-loop system and show that the finite-time convergence to the terminal set is achieved as the uncertainty of the GP model becomes smaller. Moreover, in order to reduce the uncertainty of the GP model and increase efficiency to find the optimal solution, we provide an overall learning-based event-triggered MPC algorithm based on an iterative task. Finally, we demonstrate the proposed approach through a tracking control problem.