Event-triggered Control for Nonlinear Systems with Center Manifolds

TL;DR

This paper develops event-triggered control strategies for nonlinear systems with center manifolds, ensuring stability and boundedness while reducing control updates, demonstrated through three illustrative examples including a Mobile Inverted Pendulum.

Contribution

It introduces new event-triggering conditions based on local input-to-state stability for nonlinear systems with center manifolds, including cases with approximate manifold knowledge.

Findings

Ensures local ultimate boundedness of trajectories.

Guarantees a positive lower bound on inter-event times.

Demonstrates effectiveness through three examples, including a Mobile Inverted Pendulum.

Abstract

In this work, we consider the problem of event-triggered implementation of control laws designed for the local stabilization of nonlinear systems with center manifolds. We propose event-triggering conditions which are derived from a local input-to-state stability characterization of such systems. The triggering conditions ensure local ultimate boundedness of the trajectories and the existence of a uniform positive lower bound for the inter-event times. The ultimate bound can be made arbitrarily small, but by allowing for smaller inter-event times. Under certain assumptions on the controller structure, local asymptotic stability of the origin is also guaranteed. Two sets of triggering conditions are proposed, that cater to the cases where the exact center manifold and only an approximation of the center manifold is computable. The closed-loop system exhibits some desirable properties when the exact knowledge of the center manifold is employed in checking the triggering conditions. Three illustrative examples that explore different scenarios are presented and the applicability of the proposed methods is demonstrated. The third example concerns the event-triggered implementation of a position stabilizing controller for the open-loop unstable Mobile Inverted Pendulum (MIP) robot.