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1
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Non-quadratic performance design for Takagi-Sugeno fuzzy systems

100%
Bernal M., Hušek P.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 3
383-391
EN
This paper improves controller synthesis of discrete Takagi-Sugeno fuzzy systems based on non-quadratic Lyapunov functions, making it possible to accomplish various kinds of control performance specifications such as decay rate conditions, requirements on control input and output and disturbance rejection. These extensions can be implemented via linear matrix inequalities, which are numerically solvable with commercially available software. The controller design is illustrated with an example.
2
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Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control

100%
Qi R., Brdys M.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 4
619-630
EN
In this paper, a unified nonlinear modeling and control scheme is presented. A self-structuring Takagi-Sugeno (T-S) fuzzy model is used to approximate the unknown nonlinear plant based on I/O data collected on-line. Both the structure and the parameters of the T-S fuzzy model are updated by an on-line clustering method and a recursive least squares estimation (RLSE) algorithm. The rules of the fuzzy model can be added, replaced or deleted on-line to allow a more flexible and compact model structure. The overall controller consists of an indirect adaptive controller and a supervisory controller. The former is the dominant controller, which maintains the closed-loop stability when the fuzzy system is a good approximation of the nonlinear plant. The latter is an auxiliary controller, which is activated when the tracking error reaches the boundary of a predefined constraint set. It is proven that global stability of the closed-loop system is guaranteed in the sense that all the closed-loop signals are bounded and simulation examples demonstrate the effectiveness of the proposed control scheme.
3
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Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure

100%
Boukezzoula R., Galichet S., Foulloy L.
International Journal of Applied Mathematics and Computer Science
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2007
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tom 17
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nr 2
233-248
EN
This paper examines the inverse control problem of nonlinear systems with stable dynamics using a fuzzy modeling approach. Indeed, based on the ability of fuzzy systems to approximate any nonlinear mapping, the nonlinear system is represented by a Takagi-Sugeno (TS) fuzzy system, which is then inverted for designing a fuzzy controller. As an application of the proposed inverse control methodology, two popular control structures, namely, feedback linearization and Nonlinear Internal Model Control (NIMC) are investigated. Moreover, the paper points out that, under some conditions, both of the control structures are equivalent and naturally implement a Smith predictor in the presence of time delays.
4
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Stability of softly switched multiregional dynamic output controllers with a static antiwindup filter: A discrete-time case

100%
Zubowicz T., Brdyś M.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 1
65-73
EN
This paper addresses the problem of model-based global stability analysis of discrete-time Takagi-Sugeno multiregional dynamic output controllers with static antiwindup filters. The presented analyses are reduced to the problem of a feasibility study of the Linear Matrix Inequalities (LMIs), derived based on Lyapunov stability theory. Two sets of LMIs are considered candidate derived from the classical common quadratic Lyapunov function, which may in some cases be too conservative, and a fuzzy Lyapunov function candidate, which has been proven to significantly reduce the conservatism level, although at the cost of increasing the number of LMIs. Two numerical examples illustrate the main result.
5
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Fuzzy and neural control of an induction motor

88%
Denai M. A., Attia S. A.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 2
221-233
EN
This paper presents some design approaches to hybrid control systems combining conventional control techniques with fuzzy logic and neural networks. Such a mixed implementation leads to a more effective control design with improved system performance and robustness. While conventional control allows different design objectives such as steady state and transient characteristics of the closed loop system to be specified, fuzzy logic and neural networks are integrated to overcome the problems with uncertainties in the plant parameters and structure encountered in the classical model-based design. Induction motors are characterised by complex, highly non-linear and time-varying dynamics and inaccessibility of some states and outputs for measurements, and hence can be considered as a challenging engineering problem. The advent of vector control techniques has partially solved induction motor control problems, because they are sensitive to drive parameter variations and performance may deteriorate if conventional controllers are used. Fuzzy logic and neural network-based controllers are considered as potential candidates for such an application. Three control approaches are developed and applied to adjust the speed of the drive system. The first control design combines the variable structure theory with the fuzzy logic concept. In the second approach neural networks are used in an internal model control structure. Finally, a fuzzy state feedback controller is developed based on the pole placement technique. A simulation study of these methods is presented. The effectiveness of these controllers is demonstrated for different operating conditions of the drive system.
6
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What is not clear in fuzzy control systems

75%
Piegat A.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
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nr 1
37-49
EN
The paper presents a number of unclear, unsolved or partly solved problems of fuzzy logic, which hinder precise transformation of expert knowledge about proper control of a plant in a fuzzy controller. These vague problems comprise the realization of logical and arithmetic operations and another basic problem, i.e., the construction of membership functions. The paper also indicates how some of the above problems can be solved.
7
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Fuzzy-arithmetic-based Lyapunov synthesis in the design of stable fuzzy controllers: A computing-with-words approach

63%
Zhou C.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 3
411-421
EN
A novel approach to designing stable fuzzy controllers with perception-based information using fuzzy-arithmetic-based Lyapunov synthesis in the frame of computing with words (CW) is presented. It is shown that a set of conventional fuzzy control rules can be derived from the perception-based information using the standard-fuzzy-arithmetic-based Lyapunov synthesis approach. On the other hand, a singleton fuzzy controller can be devised by using a constrained-fuzzy-arithmetic-based Lyapunov synthesis approach. Furthermore, the stability of the fuzzy controllers can be guaranteed by means of the fuzzy version of Lyapunov stability analysis. Moreover, by introducing standard and constrained fuzzy arithmetic in CW, the 'words' represented by fuzzy numbers could be efficiently manipulated to design fuzzy controllers. The results obtained are illustrated with the design of stable fuzzy controllers for an autonomous pole balancing mobile robot.
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