Fuzzy feedback system analysis using transition matrices
ABSTRACT An analytical characterization of fuzzy feedback systems based on transition matrices is carried out in this paper. The analysis faces both systems which use linear operators (sum and product) and those based on the max–min operators. We focus on the asymptotic trend of the system when the external input is held constant; such study becomes a matrix convergence problem by means of the transition matrices that define the system behavior. For the non-linear case a sufficient condition of convergence of the system (that, in particular, avoids oscillations) is demonstrated.
Article: Fuzzy control with fuzzy inputs[Show abstract] [Hide abstract]
ABSTRACT: This paper is concerned with the use of fuzzy inputs in fuzzy logic controllers. A precise representation of fuzzy logic controllers by means of mappings is used to introduce different ways for dealing with fuzzy inputs. Two types of fuzzy inputs are presented and their potential use in fuzzy control is discussed. The proposed concepts are applied to control a first order process with a PI controller. This simple process is chosen to clearly illustrate the behavior of the closed-loop system using fuzzy inputs for fuzzy reference and fuzzy measurement. Finally, a nonlinear process is used to illustrate the effects of fuzzy inputs on a more complex system. Although it is sometimes speculated that fuzzy inputs may improve the behavior of fuzzy controllers, experiments developed in this paper show this point is not straightforward and that the relevance of fuzzy inputs should be questioned in closed-loop fuzzy control.IEEE Transactions on Fuzzy Systems 09/2003; 11(4-11):437 - 449. DOI:10.1109/TFUZZ.2003.814831 · 6.31 Impact Factor
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ABSTRACT: This paper presents the identification of non-linear dynamical systems by recurrent fuzzy system models. Two types of recurrent fuzzy systems (RFS) models are discussed, the Takagi-Sugeno-Kang (TSK) type and the linguistic or Mamdani type. Both models are equivalent and the latter model may be represented by a fuzzy finite-state automaton. An identification procedure is proposed based on a standard general purpose genetic algorithm. First, the TSK rule parameters are estimated and, in a second step, the TSK model is converted into an equivalent linguistic model. The parameter identification is evaluated in some benchmark problems for non-linear system identification described in literature. The results show that RFS models achieve good numerical performance while keeping the interpretability of the actual system dynamics.IEEE Transactions on Fuzzy Systems 03/2008; 16(1):213-224. DOI:10.1109/TFUZZ.2007.902015 · 6.31 Impact Factor
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ABSTRACT: A matrix procedure to obtain a hierarchical decomposition of a multiple-input-single-output (MISO) fuzzy system is proposed. It is based on the fast inference using transition matrices (FITM) framework recently described. The resulting hierarchical system is totally equivalent to the original one in terms of input-output relation. A study of the rule-reduction capability of this system is carried out. Additionally, this paper describes a rule-base definition procedure of each of the systems resulting within the hierarchy. This procedure is based on closed-form analytical expressions and it does not need any manual interaction.IEEE Transactions on Fuzzy Systems 07/2008; 16(3-16):585 - 599. DOI:10.1109/TFUZZ.2007.905905 · 6.31 Impact Factor