Simplified Output Feedback Stabilization for Interconnected Systems Based on Dynamic Surface Control

A novel simplified adaptive fuzzy decentralized re gulation approach is proposed for a class of output-feedback large-scale nonlinear systems wi th unknown interconnections. Each subsystem is needed only one fuzzy approximator, so the number o f approximators employed equal to the number of subsystems of the whole large-scale systems. Thi is different from the existing results, which are used to employ much more than one approximator in e ach subsystem. It is proved that the proposed design approach is able to guarantee semi-global un iform ultimate boundedness (SGUUB) of all signals in the closed-loop system, with arbitrary s mall regulating error by appropriately choosing design constants. Introduction In the past several years, active research has been carried out based on approximators in adaptive backstepping control or adaptive dynamic surface co ntrol (DSC), which employed FLS or neural network (NN) to approximate system unknown nonlinea rities, and various significant results were developed in [1,2,3,4,5]. However, one limitation i s that too many approximators are used in the controller design procedure. For nth-order SISO systems [1,2], there usually needed a t least n approximators to compensate the system unknown nonl inearities, then n or even more unknown parameters and approximation errors will be brought into the controller design procedure, which causes the employment of the same amount of adaptiv e laws in the closed-loop systems. For large-scale systems comprised of N subsystems [3,4,5] ( nith-order subsystems, 1, , i N = . ), approximators needed are usually more than 1 N i i n = Σ . The existence of so many approximators makes the controller structure more complicated. In [6], a simplified regulation method was proposed and tried to solve this problem, but it is only for SIS O systems, and the problem “explosion of complexity” which exists in the backstepping design procedure have not been avoided. In the large-scale system control theory, the most difficu lt problem which has to be faced with is how to dea l with the unknown interconnections, which are mixed up with all of the subsystem output, so the result mentioned before can not be used directly. In this paper, we focus our attention on how to com pensate the unknown interconnections through a more simplified way. Firstly, each subsystem is n eeded only one fuzzy approximator, so the approximators employed equal to the number of subsy stems of the whole large-scale systems. Then only one adaptive law is needed there for unknown p arameter and error bound in each subsystem. Furthermore, through lumping the items which have t he same argument, the input variable of each fuzzy approximator is declined to one. Thus, the nu mber of fuzzy IF-THEN rules is also declined, and the controller structure is further simplified indi rectly. Based on Lyapunov stability theory, it is proved that the proposed simplified adaptive fuzzy decentralized DSC (AFDDSC) design procedure can guarantee all the closed-loop signals semi-glob ally uniformly ultimately bounded (SGUUB) and the errors converging to an arbitrary small residua l set around the origin. Throughout this paper, ∗ denotes the 2-norm of ∗ , ∗̂ denotes the estimate of ∗ , ˆ ∗ = ∗−∗ ɶ , and ( ) max λ ∗ denote the largest eigenvalue of a positive defini t matrix ∗ . Applied Mechanics and Materials Online: 2011-05-03 ISSN: 1662-7482, Vols. 55-57, pp 992-997 doi:10.4028/www.scientific. net/AMM.55-57.992 © 2011 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific. net. (Semanticscholar.org-18/03/20,17:39:27) Problem statement and preliminaries Consider an uncertain large-scale output-feedback s ystem comprised of N subsystems interconnected by their outputs. The i'th subsystem ( ) 1, i i N Σ = . is given by ( ) ( ) , , 1 . 1 2