scholarly journals How to vary the input space of a TS fuzzy model: a TP model transformation based approach

2020 ◽  
pp. 1-1
Author(s):  
Peter Baranyi
Keyword(s):  
Model Transformation ◽  
Fuzzy Model ◽  
Input Space ◽  
Ts Fuzzy Model

scholarly journals Extension of the Multi-TP Model Transformation to Functions with Different Numbers of Variables

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Péter Baranyi
Keyword(s):  
Model Transformation ◽  
Fuzzy Model ◽  
Singular Value ◽  
Model Transformations ◽  
Extended Version ◽  
Ts Fuzzy Model ◽  
Fuzzy Models ◽  
Trade Offs ◽  
Value Decomposition ◽  
And Control

The tensor product (TP) model transformation defines and numerically reconstructs the Higher-Order Singular Value Decomposition (HOSVD) of functions. It plays the same role with respect to functions as HOSVD does for tensors (and SVD for matrices). The need for certain advantageous features, such as rank/complexity reduction, trade-offs between complexity and accuracy, and a manipulation power representative of the TP form, has motivated novel concepts in TS fuzzy model based modelling and control. The latest extensions of the TP model transformation, called the multi- and generalised TP model transformations, are applicable to a set functions where the dimensionality of the outputs of the functions may differ, but there is a strict limitation on the dimensionality of their inputs, which must be the same. The paper proposes an extended version that is applicable to a set of functions where both the input and output dimensionalities of the functions may differ. This makes it possible to transform complete multicomponent systems to TS fuzzy models along with the above-mentioned advantages.

scholarly journals Further results on robust fuzzy dynamic systems with LMI D-stability constraints

2014 ◽  
Vol 24 (4) ◽  
pp. 785-794 ◽  
Author(s):  
Wudhichai Assawinchaichote
Keyword(s):  
Dynamic Systems ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Local System ◽  
Linear Matrix ◽  
Fuzzy Modelling ◽  
Ts Fuzzy Model ◽  
Input Noise ◽  
Takagi Sugeno

Abstract This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

Decay rate performance approach for stabilization continuous fuzzy models using their discretized forms

2015 ◽  
Vol 8 (4) ◽  
pp. 383-400
Author(s):  
Ameni Ellouze ◽  
François Delmotte ◽  
Jimmy Lauber ◽  
Mohamed Chtourou ◽  
Mohamed Ksantini
Keyword(s):  
Decay Rate ◽  
Discrete Model ◽  
Fuzzy Model ◽  
Performance Criterion ◽  
Rate Performance ◽  
Content Type ◽  
Ts Fuzzy Model ◽  
Fuzzy Models ◽  
Discretization Step ◽  
The Stability

Purpose – The purpose of this paper is to deal with the stabilization of the continuous Takagi Sugeno (TS) fuzzy models using their discretized forms based on the decay rate performance approach. Design/methodology/approach – This approach is structured as follows: first, a discrete model is obtained from the discretization of the continuous TS fuzzy model. The discretized model is obtained from the Euler approximation method which is used for several orders. Second, based on the decay rate stabilization conditions, the gains of a non-PDC control law ensuring the stabilization of the discrete model are determined. Third by keeping the values of the gains, the authors determine the values of the performance criterion and the authors check by simulation the stability of the continuous TS fuzzy models through the zero order hold. Findings – The proposed idea lead to compare the performance continuous stability results with the literature. The comparison is, also, taken between the quadratic and non-quadratic cases. Originality/value – Therefore, the originality of this paper consists in the improvement of the continuous fuzzy models by using their discretized models. In this case, the effect of the discretization step on the performances of the continuous TS fuzzy models is studied. The usefulness of this approach is shown through two examples.

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