Fuzzy Sets and Systems 157 (2006) 2241 – 2258 www.elsevier.com/locate/fss Adaptive fuzzy controller: Application to the control of the temperature of a dynamic room in real time I. Rojas ∗ , H. Pomares, J. Gonzalez, L.J. Herrera, A. Guillen, F. Rojas, O. Valenzuela Department of Computer Architecture and Computer Technology, Facultad de Ciencias, Campus Universitario Fuentenueva s/n, E-18071, University of Granada, Spain Received 17 June 2004; received in revised form 4 January 2006; accepted 4 March 2006 Available online 30 March 2006 Abstract This paper presents a direct adaptive fuzzy controller for unknown monotonic nonlinear systems, thus not requiring the system model, but only a little information about it: the plant monotonicity and its delay. Without any off-line pre-training, the algorithm achieves very high control performance through a three-stage algorithm: (1) output scale factor, (2) adaptation of the fuzzy rule consequents and (3) optimization of the position of the membership functions. The design is simple, in the sense that both the membership functions and the rule-base can be initialized from arbitrary values. It can be applied to a large class of monotonic dynamic or static plants, due the fact that the system is able to modify its behaviour in real time, i.e., during the control process. © 2006 Elsevier B.V. All rights reserved. Keywords: Fuzzy control; Adaptive fuzzy controller; Real-time application 1. Introduction Just as fuzzy systems can be described as ‘computing with words rather than numbers’, fuzzy control can be described as ‘control with sentences rather than equations’ [22]. It is more natural to use sentences or rules in, for instance, operator-controlled plants with the control strategy written in terms of if–then clauses [8]. Generally, the model obtained by fuzzy logic systems depends linearly on unknown parameters that lead to the use of a Lyapunov- based learning scheme. It was first applied with success in the domain of neural networks because of their learning ability and universal approximating power. Hence, the combination of learning, adaptivity and uncertainty enabled researchers to derive adaptive (or neuro) fuzzy controllers. These new models ensure the stability of the overall system and the convergence of the plant output towards a given reference signal. If the controller furthermore adjusts the control strategy without human intervention it is adaptive. While non-adaptive fuzzy control has proven its value in some applications, it is sometimes difficult to specify the rule-base for some plants, or the need could arise to tune the rule-base parameters if the plant changes. This provides the motivation for adaptive fuzzy control, where the focus is on the automatic on-line synthesis and tuning of the fuzzy controller parameters i.e., the use of on-line data from which the fuzzy controller can continually ‘learn’, which will ensure that the performance objectives are met. ∗ Corresponding author. Tel.: +34 958 246128; fax: +34 958 248993. E-mail address: irojas@atc.ugr.es (I. Rojas). 0165-0114/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fss.2006.03.006