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steady-state error can be eliminated by including an integral term in the linear part of the controller (19).

TLDR
In this article, a neural network was proposed for adaptive output feedback control of uncertain nonlinear systems using neural networks and a simple linear observer was introduced to estimate the derivatives of the tracking error.
Abstract
IX. SUMMARY A new approach has been proposed for adaptive output feedback control of uncertain nonlinear systems using neural networks. A simple linear observer was introduced to estimate the derivatives of the tracking error. These estimates are used as inputs to the neural network and in the adaptation laws as an error signal. Ultimate boundedness of all error signals was proven by Lyapunov’s direct method. Simulations of a second-order system illustrated the theoretical results.

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References
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Book

Nonlinear and adaptive control design

TL;DR: In this paper, the focus is on adaptive nonlinear control results introduced with the new recursive design methodology -adaptive backstepping, and basic tools for nonadaptive BackStepping design with state and output feedbacks.
Book

Linear Optimal Control Systems

TL;DR: In this article, the authors provide an excellent introduction to feedback control system design, including a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems.
Book

Singular perturbation methods in control : analysis and design

TL;DR: This SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications.
Book

Constructive Nonlinear Control

TL;DR: In this article, the authors introduce the concept of passive design tools as a design tool for adaptive control and propose a cascade design with feedback passivation of Cascades and partial-state feedback.
Journal ArticleDOI

The optimal linear-quadratic time-invariant regulator with cheap control

TL;DR: In this article, the infinite-time linear-quadratic regulator is considered as the weighting on the control energy tends to zero (cheap control), and a study is made of the qualitative behavior of the limiting optimal state and control trajectories.
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