Adaptive Event-Triggered MPC for Linear Parameter-Varying Systems with State Delays, Actuator Saturation and Disturbances

Abstract

This paper proposes a unified adaptive event-triggered model predictive control (ETMPC) scheme for linear parameter-varying (LPV) systems subject to state delays, actuator saturation, and external disturbances. In existing studies, only a limited number of ETMPC methods have attempted to address either state delays or actuator saturation, and even these few methods typically lack co-design optimization between adaptive event-triggering mechanisms and the control law. To overcome these limitations, this paper presents a Lyapunov-Krasovskii-based adaptive ETMPC strategy that enables the co-design optimization of both the triggering mechanism and the controller. Specifically, the event-triggering parameter matrix is adaptively optimized by embedding an internal adaptive variable within the Lyapunov-Krasovskii-like function. Furthermore, the actuator saturation nonlinearity is transformed into a convex hull representation. The infinite-horizon robust optimization problem is reformulated as a convex optimization problem with linear matrix inequality (LMI) constraints. Invariant set constraints are introduced to ensure recursive feasibility, and mean-square input-to-state stability (ISS) under multiple uncertainties is rigorously established. Simulations on an industrial electric heating system validate the proposed method's effectiveness in reducing communication load.