Controllability of Fuzzy Control Systems

Gupta, Madan M.; Trojan, G. M.; Kiszka, Jerzy B.

doi:10.1109/tsmc.1986.289262

Cited by 30 publications

(6 citation statements)

References 7 publications

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“…Given an input, the fuzzy relational equation is resolved to produce an output by using r y (i) = max[tnin(y R (JJlr x (J))] (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) wherey (i) is the degree of truth that the rth output set applies, y x (i) is the degree of truth that the input belongs to the yth input set,y R (i,j) is the relational array entry representing the degree of truth of a cause-and-efFect relationship between the/th input set and the rth output set. Example 6.3.…”

Section: Algorithm 61mentioning

confidence: 99%

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Fuzzy Control Systems

Cai¹

1997

Intelligent Control: Principles, Techniques and Applications

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Fuzzy control has been an active research and application area of intelligent controls for the past twenty years. As we have mentioned in Section 1.2.2, fuzzy sets were first proposed by Zadeh [49] as a method of handling real world classes of objects. Since then, a great amount of research efforts has been carried out both in the theoretical investigations and practical applications of fuzzy sets and fuzzy control.Fuzzy control is a kind of control approach that uses the fuzzy set theory. The usefulness of fuzzy control can be considered in two respects. On one hand, fiizzy control offers a novel mechanism to implement such control laws that are often knowledge-based (rule-based) or even in linguistic description. On the other hand, fuzzy control provides an alternative methodology to facilitate the design of nonlinear controllers for such plants being controlled, that are usually uncertain and very difficult to cope with by using conventional nonlinear control theory.Expert Control Systems and Fuzzy Logic Control (FLC) systems have certainly one thing in common: both aim to model human experience, human decision-making behavior. There are, however, clear differences between expert control systems and fuzzy logic control systems: (1) The existing FLC systems originated in control engineering rather than in Artificial Intelligence; (2)~FLC models are mostly rule-based systems; (3) The application domains of FLC are narrower than those of expert control systems; (4) The rules of FLC systems are generally not extracted from the human expert through the system but formulated explicitly by the FLC designer. For these reasons, it is necessary to discuss the fiizzy control system separately from the expert control systems in this chapter.In this section, the foundation of fuzzy set and fiizzy logic for control is briefly reviewed at first, then the types, structure, design and properties of fuzzy logic controller are presented, and an application example of FLC is demonstrated at last.

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Section: Algorithm 61mentioning

confidence: 99%

“…Gupta proposed a method for describing system controllability of fiizzy relation in the energetic controllable point of view [13]. i.e., u l ,---u n eV 2 and D(x n+l )<s hold, then x is also controllable for energy L.…”

Section: Related Theories Of Fuzzy Systems and T-systemmentioning

confidence: 99%

Fuzzy Control Systems

Cai¹

1997

Intelligent Control: Principles, Techniques and Applications

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“…In [34], the authors introduced the idea of soft-controllability, i.e. the existence of a control sequence that forces the system to a reachable state close enough to the desired final state, and have analyzed this property using graph representations.…”

Section: Introductionmentioning

confidence: 99%

A practical test for assessing the reachability of discrete-time Takagi–Sugeno fuzzy systems

Witczak

Rotondo

Puig

et al. 2015

Journal of the Franklin Institute

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This paper provides a necessary and sufficient condition for the reachability of discrete-time Takagi-Sugeno fuzzy systems that is easy to apply, such that it constitutes a practical test. The proposed procedure is based on checking if all the principal minors associated to an appropriate matrix are positive. If this condition holds, then the rank of the reachability matrix associated to the Takagi-Sugeno fuzzy system is full for any possible sequence of premise variables, and thus the system is completely state reachable. On the other hand, if the principal minors are not positive, the property of the matrix being a block P one with respect to a particular partition of a set of integers is studied in order to conclude about the reachability of the Takagi-Sugeno system. Examples obtained using an inverted pendulum are used to show that it is easy to check this condition, such that the reachability analysis can be performed efficiently using the proposed approach.

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“…The controllability and observability analysis of dynamical systems has been an active area of research in control theory since the pioneer work of Kalman for the linear time invariant (LTI) case [1]. Since then, progress has been carried out in several directions such as the controllability/observability of a class of nonlinear systems [2][3][4][5], some types of fuzzy systems [6,7], and the structural controllability/observability of LTI systems [8][9][10], aimed at robust system monitoring.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Foundations for Efficient Structural Controllability and Observability Analysis of Complex Systems

Zufiria

Úbeda-Medina²,

Herrera-Yagüe³

et al. 2014

Mathematical Problems in Engineering

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The relationship between structural controllability and observability of complex systems is studied. Algebraic and graph theoretic tools are combined to prove the extent of some controller/observer duality results. Two types of control design problems are addressed and some fundamental theoretical results are provided. In addition new algorithms are presented to compute optimal solutions for monitoring large scale real networks.

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Controllability of Fuzzy Control Systems

Cited by 30 publications

References 7 publications

Fuzzy Control Systems

Fuzzy Control Systems

A practical test for assessing the reachability of discrete-time Takagi–Sugeno fuzzy systems

Mathematical Foundations for Efficient Structural Controllability and Observability Analysis of Complex Systems

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