Decentralized Event-Triggered Tracking of a Class of Uncertain Interconnected Nonlinear Systems Using Minimal Function Approximators

Abstract

This paper investigates a minimal-function-approximation (MFA)-based decentralized event-triggered tracking problem for uncertain interconnected systems with completely unknown nonaffine nonlinearities. It is assumed that events are triggered to transmit state variables in the sensor-to-controller channel. The existing approximation-based event-triggered control schemes for single lower-triangular nonlinear systems require multiple neural-network-based or fuzzy-based function approximators and multiple event-triggering conditions that are equal to the order of the system. Thus, all error surfaces using virtual control laws should be computed to verify the triggering conditions in the sensor part. To overcome the complexity in using these multiple function approximators and event-triggering conditions, we propose an event-triggered tracking strategy using one function approximator and one event-triggering condition for each subsystem in the decentralized control framework, regardless of the order of pure-feedback nonlinear subsystems. The proposed strategy is based on the MFA design technique and thus one event-triggering condition using a local tracking error is established for the local tracking law of each subsystem. Using the impulsive system approach and the Lyapunov stability theorem, the total closed-loop stability is analyzed rigorously and the minimum interevent times for each subsystem are derived to exclude the unexpected Zeno behavior.