Fuzzy Switching Functions Research Articles

Fuzzy super twisting algorithm dual direct torque control of doubly fed induction machine

<span>This paper proposes the fundamental aspects of hybrid nonlinear control which is composed of the super twisting algorithm (STA) based second order sliding mode control applying fuzzy logic method (FSOSMC), with pertinent simulation results for a doubly fed induction machine (DFIM) drive. To minimize chattering effect phenomenon due to Signum function employed in sliding mode algorithm, a new method is proposed. This technique consists in replacing the signum function by fuzzy switching function in the SOSMC to minimize flux and torque ripples. This FSOSMC is associated to the double direct torque control DDTC of the doubly fed induction machine (DFIM) by combining the advantages of fuzzy logic (FL) and the advantages of super-twisting sliding mode. The FSOSMC-DDTC strategy is compared with a PI-DDTC and SOSMC-DDTC. Simulation results demonstrate good efficiency and excellent robustness of the hybrid nonlinear controller.</span>

A Fuzzy Optimal Sliding-Mode Guidance for Intercepting Problem

In this paper, a novel terminal guidance law is proposed to solve the problem of exo-atmospheric interception. It is designed based on the proportional navigation (PN) and the classical optimal sliding-mode guidance (OSMG). It overcomes the shortcoming of these two traditional guidance laws and inherits their merits. Particularly, in the scenario of exoatmospheric interception, when the maneuvering information of the targets are unavailable, the proposed guidance law has superior performance than the traditional guidance law. Briefly, to enhance the interceptive performance, we introduce the optimal control and sliding-mode control methods to the guidance law for maneuvering target's interception. On the other hand, the traditional proportional navigation law is introduced to intercept the target with a constant speed. After that, a fuzzy switching function is provided to harmonize both situations above, according to the real-time estimation of maneuver. To guarantee the stability of the law, a Lyapunov based condition is obtained. Finally, different from the two-dimensional simulation in most of the literatures of terminal guidance law researches, we illustrate our method in the nonlinear discrete three-dimensional simulation environment by the Runge-Kutta method. Compared with the pure OSMG and PN, the proposed law performs better.

Fuzzy sliding mode control with a fuzzy switching function for non-linear uncertain multi-input multi-output systems

This paper presents two approaches for the fuzzy sliding mode control of uncertain and disturbed non-linear multi-input multi-output (MIMO) systems. In the first approach, the control law is deduced from a nominal model of the plant. An adaptive fuzzy system is introduced to substitute the switching control and, hence, to eliminate the chattering phenomenon. In the second approach, two other adaptive fuzzy systems are used to approximate and thereby to overcome the unavailability of the nominal model. The stability and the robustness are proven analytically in both cases, and the adaptation laws of the fuzzy systems are deduced from Lyapunov synthesis. A simulation example of a two-link robot is used for illustration.

Fuzzy sliding mode control with a fuzzy switching function for non-linear uncertain multi-input multi-output systems

This paper presents two approaches for the fuzzy sliding mode control of uncertain and disturbed non-linear multi-input multi-output (MIMO) systems. In the first approach, the control law is deduced from a nominal model of the plant. An adaptive fuzzy system is introduced to substitute the switching control and, hence, to eliminate the chattering phenomenon. In the second approach, two other adaptive fuzzy systems are used to approximate and thereby to overcome the unavailability of the nominal model. The stability and the robustness are proven analytically in both cases, and the adaptation laws of the fuzzy systems are deduced from Lyapunov synthesis. A simulation example of a two-link robot is used for illustration.

Fuzzy Three-valued Switching Functions Using Choquet Integral

Fuzzy three-valued switching functions have true, false and unknown inputs and outputs values. The functions are calculated by Choquet integral whose fuzzy measure values are assigned from normal three-valued switching functions. The functions are extension of normal three-valued functions and satisfy the monotonicity with respect to vagueness.

On the complexity of growth of the number of distinct fuzzy switching functions

Several attempts have been made to enumerate fuzzy switching (FSF's) and to develop upper and lower bounds for the number of FSF's of n variables in an effort to better understand the properties and the complexity of FSF's. Previous upper bounds are 2 4n [9] and 2 2–3n—2n—1 [7]. It has also been shown that the exact numbers of FSF's of n variables for n = 0, 1, 2, 3, and 4 are 2, 6, 8, 84, 43 918 and 160 297 985 276 respectively. This paper will give a brief overview of previous approaches to the problem, study some of the properties of fuzzy switching functions and give improved upper and lower bounds for a general n.

Multivalued Logic and Fuzzy Logic--Their Relationship, Minimization, and Application to Fault Diagnosis

The k-valued Kleene functions over Kleene algebra (instead of over Post algebra) are defined. Multivalued logic and fuzzy logic are studied in the light of lattice theory. It is shown that all Kleene k-valued logic (k = 3 or more) have the same algebraic structure as fuzzy logic through lattice isomorphism. As a by-product, an asymptotic formula and upper bound for enumeratinlg fuzzy switching functions of n variables is obtained. Some conditions for minimizing Kleene functions are discussed, and an efficient generalized Karnaught map method is described. An application is made of the above Kleene multivalued logic to the fault diagnosis of combinational circuits. The fault norm of a combinational circuit is introduced and it is shown that this norm contains all the information about the fault situation of the circuit, and can hence be used to solve such problems as fault analysis, fault diagnosis, and detection of circuit redundance and fault masking.

Enumerating fuzzy switching functions and free kleene algebras

We investigate the free Kleene algebra on n free generators, FK( n). This algebra is essentially the same as the set of n-variable fuzzy switching functions. The cardinality of FK( n) has been previously determined only for n = 1, 2, and 3. We present a general method for enumeration problems of this kind. We show FK(4) has 160,297,985,276 elements. The final section contains new upper and lower bounds for the cardinality of FK( n). We also consider the number of regular functions and show that there are 11,197,129,615, and 430,904,428,717 such functions in 1, 2, 3, and 4 variables.

A Method for the Generation and Processing of Dyadic Indexed Data

The elements of an array of 2n data are indexed so that adjacent elements have Hamming distance 1. Based on this indexing a class of invertible fast in-place transformations is developed. The transform coefficients depend on the Hamming distance between the indexes of input data. A class of similar transformations exists in the Walsh-Hadamard domain. Three transform operations are discussed in detail: dyadic shift transform, a subsuming and averaging transformation and a weighting operation. Applications of the method are in the processing of Boolean and fuzzy switching functions, image analysis, etc.

Decomposable fuzzy-valued switching functions

Functional decomposition is the process of expressing a function of n variables as a composition of a number of functions, each depending on less than n variables. If the function to be decomposed is a Boolean function, then the methods proposed by Ashenhurst and Curtis can be used [2]-[6]. However, if the function is a fuzzy-valued function, then a different method is necessary to decompose the function. In this paper, after the basic definitions of fuzzy algebra are given, a brief review of the work in fuzzy switching logic is presented. The insufficiencies of Boolean methods and a previous method by Kandel [23] for the decomposition of a fuzzy switching function are discussed. A new theorem for determining if a function possesses a fuzzy simple disjunctive decomposition as well as a method for decomposing such a function are developed. Some practical applications for the decomposition of fuzzy switching functions are presented along with some open questions on this topic.

On the representation and enumeration of fuzzy switching functions

This paper examines the properties of fuzzy switching functions of n variables with the help of combinatorial theory. A new concept of canonical representation is explained, and it is shown that any fuzzy switching function can be canonically represented as a sum of K ⩽ N max fundamental phrases, which form an antichain in the poset P of all fundamental phrases. Also, an algorithm to enumerate the distinct fuzzy switching functions and two formulae for the upper and lower bounds, which are better than those given by C. Clark, M. Ben-David, and A. Kandel [ Fuzzy Sets Systems 5 , 69–81 (1981)] and T. Kameda and E. Sadeh [ Inform. Contr. 35 , 139–145 (1977)], are given.

On the enumeration of distinct fuzzy switching functions

This paper entails the development of bound equations on the number of minimized fuzzy switching functions. A triangular matrix representing the transitivity between fundamental fuzzy phrases is discussed and applied in the enumeration process. Improved upper and lower bounds have been developed by use of the transitivity matrix. In addition, an algorithm is described to calculate the number of distinct fuzzy switching functions for any number of variables.

Simplification of fuzzy switching functions

This paper is concerned with the study of simplification of fuzzy switching functions. A novel algorithm for generating all fuzzy prime implicants is introduced, followed by a new method of simplification of fuzzy switching functions. This algorithm is then reduced to a simple algorithm that produces only those fuzzy prime implicants that are essential. There areonly two other valid techniques for the minimization of fuzzy switching functions in the literature,(1,2) and those methods are not very suitable for computerized application. Thus, the principal advantages of this technique are the new concept of direct simplification via essential fuzzy prime implicants (without generation of all of the fuzzy prime implicants), and the fact that the algorithm is the first one to be suitable for efficient computer implementation.

A note on the simplification of fuzzy switching functions

This note is concerned with the modification of the definition of fuzzy consensus. The modified version is used to find the set of all fuzzy prime implicants of a fuzzy switching function as defined previously. The fuzzy algebra used to derive these functions satisfies the set of axioms of a distributive lattice with unique identities under the operators of maximum and minimum as described earlier.

Fuzzy Maps

A graphical scheme (map) for representation and manipulation of fuzzy switching functions is described. Properties of the map and relationships between represented implicants are discussed. Emphasis is placed on illustrations of the use of the map in manipulation and minimization of fuzzy switching functions.

On the Properties of Fuzzy Switching Functions

Abstract A strictly binary approach to the treatment of switching circuits today is not always adequate to describe systems in the real world. This approach is partly due, to the relative simplicity of designing binary switching systems, and to the fact that basic switching modules in common use are two-positional. Consequently, every variable in Boolean logic is assumed to be two-valued. However, because of real-world constraints, the attributes of system variables are often ambiguously defined. In other words, quite often variables might have values other than falsehood and truth. Cases with such attributes arise, for example in artifical intelligence and related subjects. Ever since Zadeh introduced the idea of fuzzy set theory [11 by utilizing the concept of membership grade, a number of authors have been concerned with the analysis and applications of fuzzy models. Especially, the relation of fuzzy to switching systems have been discussed in [2]–[12] and by other researchers in relation to other topics. In this paper we are concerned with the study of fuzzy switching functions and their properties. Special attention is devoted to their minimization, enumeration, and their application to Boolean static hazard detection.

A Note on the Simplification of Fuzzy Switching Functions

Abstract This note is concerned with the modification of the definition of fuzzy consensus. The modified version is used to find the set of all fuzzy prime implicants of a fuzzy switching function as defined previously. The fuzzy algebra used to derive these functions satisfies the set of axioms of a distributive lattice with unique identities under the operators of maximum and minimum as described earlier.