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: 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
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ABSTRACT: In this paper, we propose a new method for collision handling between 3-D deformable (organs) and rigid (surgical tools) objects valid for nonstructured interaction scenes and, specifically, for laparoscopic surgery simulators. During the simulation step, vertices of the organ detected as collided must be accurately shifted out of the tool to elude a visual interpenetration. The proposed approach obtains the new position of each collided vertex of the organ taking into account both kinematic information of the surgical tool and geometric information of the organ surface that surrounds the vertex under analysis. Three parameters inferred from a fuzzy feedback system weigh the nature of the tool motion with respect to the organ. Experimental results show that the solution proposed in this paper is able to avoid the interpenetration among the multiple colliding points efficiently with physically and spatially coherent results.IEEE transactions on information technology in biomedicine: a publication of the IEEE Engineering in Medicine and Biology Society 07/2009; 13:451-457. DOI:10.1109/TITB.2009.2016838 · 2.07 Impact Factor