A Control Lyapunov Function Approach to Event-Triggered Parameterized Control for Discrete-Time Linear Systems

TL;DR

This paper introduces an event-triggered control strategy for discrete-time linear systems using a control Lyapunov function, optimizing control updates to ensure stability and efficiency under disturbances.

Contribution

It presents a novel event-triggered parameterized control method with stability guarantees and reduced communication, applicable to systems with external disturbances.

Findings

Guarantees global uniform ultimate boundedness of system trajectories.

Ensures non-trivial inter-event times to reduce control updates.

Demonstrates improved performance over existing methods through numerical examples.

Abstract

This paper proposes an event-triggered parameterized control method using a control Lyapunov function approach for discrete time linear systems with external disturbances. In this control method, each control input to the plant is a linear combination of a fixed set of linearly independent scalar functions. The controller updates the coefficients of the parameterized control input in an event-triggered manner so as to minimize a quadratic cost function subject to quadratic constraints and communicates the same to the actuator. We design an event-triggering rule that guarantees global uniform ultimate boundedness of trajectories of the closed loop system and non-trivial inter-event times. We illustrate our results through numerical examples and we also compare the performance of the proposed control method with other existing control methods in the literature.