Event-Sampled Direct Adaptive NN Output-and State-Feedback Control of Uncertain Strict-Feedback System


In this paper, a novel event-triggered implementation of a tracking controller for an uncertain strict-feedback system is presented. Neural networks (NNs) are utilized in the backstepping approach to design a control input by approximating unknown dynamics of the strict-feedback nonlinear system with event-sampled inputs. The system state vector is assumed to be unknown and an NN observer is used to estimate the state vector. By using the estimated state vector and backstepping design approach, an event-sampled controller is introduced. As part of the controller design, first, input-to-state-like stability for a continuously sampled controller that has been injected with bounded measurement errors is demonstrated, and subsequently, an event-execution control law is derived, such that the measurement errors are guaranteed to remain bounded. Lyapunov theory is used to demonstrate that the tracking errors, the observer estimation errors, and the NN weight estimation errors for each NN are locally uniformly ultimately bounded in the presence bounded disturbances, NN reconstruction errors, as well as errors introduced by event sampling. Simulation results are provided to illustrate the effectiveness of the proposed controllers.


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center


This work was supported in part by NSF ECCS under Grant 1406533 and in part by the Intelligent Systems Center, MST, Rolla.

Keywords and Phrases

Adaptive control systems; Backstepping; Errors; Feedback; Feedback control; Measurement errors; State feedback; Uncertainty analysis; Back-stepping approaches; Bounded disturbances; Neural networks (NNS); Reconstruction error; Strict-feedback nonlinear systems; Tracking controller; Uncertain strict-feedback systems; Uniformly ultimately bounded; Controllers; Event sampling; Lyapunov method; Observer; Output feedback

International Standard Serial Number (ISSN)

2162-237X; 2162-2388

Document Type

Article - Journal

Document Version


File Type





© 2018 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 May 2018