Engineering Applications of Artificial Intelligence 20 (2007) 1125–1132 Decentralized adaptive recurrent neural control structure Victor H. Benitez, Edgar N. Sanchez à , Alexander G. Loukianov à CINVESTAV, Unidad Guadalajara, Apartado Postal 31-438, Plaza la Luna, Guadalajara, Jalisco C.P. 45091, Mexico Received 17 March 2006; received in revised form 9 November 2006; accepted 13 February 2007 Available online 25 April 2007 Abstract This paper presents a novel decentralized variable structure neural control approach for large-scale uncertain systems, which is developed using recurrent high-order neural networks (RHONN). It is assumed that each subsystem belongs to a class of block- controllable nonlinear systems whose vector fields includes interconnection terms, which are bounded by nonlinear functions. A decentralized RHONN structure and the respective learning law are proposed in order to approximate online the dynamical behavior of each nonlinear subsystem. The control law, which is able to regulate and to track the desired reference signals, is designed using the well- known variable structure theory. The stability of the whole system is analyzed via the Lyapunov methodology. The applicability of the proposed decentralized identification and control algorithm is illustrated via simulations as applied to an interconnected double inverted pendulum. r 2007 Elsevier Ltd. All rights reserved. Keywords: Variable structure control; Nonlinear systems; Recurrent neural networks; Large-scale systems; Lyapunov approach 1. Introduction The decentralized control approach often arises from the high dimension of the system to be controlled, the physical inability for subsystem information exchange, the lack of computing capabilities required for a single central controller and the uncertainty in measuring parameters values within a large-scale system. Typical examples where decentralized control approach can be applied arises in different kinds of industries, systems and processes. The process industry, such as the chemical one, includes a broad range of large-scale processes: bulk petrochemicals, pulp and paper and cement are examples of them. Moreover, there exist systems whose dynamical behavior changes according to unknown external disturbances or due to parameter variations. In a system of couple water reservoirs, for example, whose levels have to be controlled, effects, due to the dynamical interactions between the reservoirs and the uncertainties relative to human con- sumptions and inflow variations from the environment, need to be considered. In a multi-area power system, whose goal is to provide energy to many enterprisers and private consumers, there are dynamical variations due to changes in loads, new interconnections with other networks, changes in parameter due to saturation and operational conditions, etc. Numerous techniques and approaches are popular in industry in order to deal with large-scale systems, such as the relative gain array (RGA) (Bristol, 1966) and partial relative gain (PRG) (Haggblom, 1997). Those procedures are developed to deal with linear plants; for nonlinear plants where there exist uncertainties, parameter variations and unmodelled dynamics, the men- tioned techniques are difficult to apply. The aforemen- tioned large-scale plants have one property in common: they are all complex collections of interacting components in which change often occurs as a resulting of not predictable processes. All these examples illustrate either the lack of centralized information, or the lack of a centralized computing facility. These facts motivate the design of decentralized controllers, using only local information while guaranteeing stability for the whole system. An interesting review for the development of decentralized nonlinear adaptive control theory for ARTICLE IN PRESS www.elsevier.com/locate/engappai 0952-1976/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.engappai.2007.02.006 à Corresponding authors. Tel.: +52 3331345570; fax: +52 3331445579. E-mail address: sanchez@gdl.cinvestav.mx (E.N. Sanchez).