Adaptive Neural Network-Based Event-Triggered Control of Single-Input Single-Output Nonlinear Discrete-Time Systems


This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain nonlinear discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center


This work was supported in part by the National Science Foundation under Grant ECCS 1406533 and in part by the Intelligent Systems Center, Missouri University of Science and Technology, Rolla, MO, USA.

Keywords and Phrases

Adaptive control systems; Controllers; Digital control systems; Estimation; Uncertainty analysis; Adaptive neural network controls (ANNC); Adaptive neural networks; Approximation properties; Event-triggered controls (ETC); Nonlinear discrete-time systems; Single input and single outputs; Ultimate boundedness; Discrete time control systems; Function approximation; Neural network (NN) control

International Standard Serial Number (ISSN)

2162-237X; 2162-2388

Document Type

Article - Journal

Document Version


File Type





© 2016 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 2016