Robust Integral of Neural Network and Error Sign Control of MIMO Nonlinear Systems


This paper presents a novel state-feedback control scheme for the tracking control of a class of multi-input multioutput continuous-time nonlinear systems with unknown dynamics and bounded disturbances. First, the control law consisting of the robust integral of a neural network (NN) output plus sign of the tracking error feedback multiplied with an adaptive gain is introduced. The NN in the control law learns the system dynamics in an online manner, while the NN residual reconstruction errors and the bounded disturbances are overcome by the error sign signal. Since both of the NN output and the error sign signal are included in the integral, the continuity of the control input is ensured. The controller structure and the NN weight update law are novel in contrast with the previous effort, and the semiglobal asymptotic tracking performance is still guaranteed by using the Lyapunov analysis. In addition, the NN weights and all other signals are proved to be bounded simultaneously. The proposed approach also relaxes the need for the upper bounds of certain terms, which are usually required in the previous designs. Finally, the theoretical results are substantiated with simulations.


Electrical and Computer Engineering


This work was supported in part by the National High Technology Research and Development Program of China (863 Program) under Grant 2012AA041709 and Grant 2012AA062201, in part by the National Key Basic Research Program of China (973 Program) under Grant 2012CB720500, in part by the U.S. National Science Foundation under Grant ECCS 1128281, and in part by the Intelligent Systems Center.

Keywords and Phrases

Continuous time systems; Control theory; Errors; Feedback; Feedback control; Nonlinear feedback; Nonlinear systems; Robust control; State feedback; Asymptotic tracking; Bounded disturbances; Continuous time nonlinear systems; Controller structures; MIMO nonlinear systems; Multi-input multi-output; Neural networks (NNs); Reconstruction error; Adaptive control systems; Algorithm; Artificial neural network; Computer simulation; Feedback system; Human; Nonlinear system; Algorithms; Computer Simulation; Feedback; Humans; Neural Networks (Computer); Nonlinear Dynamics; Asymptotic stability; Lyapunov method; Nonlinear unknown systems

International Standard Serial Number (ISSN)

2162-237X; 2162-2388

Document Type

Article - Journal

Document Version


File Type





© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Dec 2015