Fuzzy tracking control of fuzzy linear dynamical systems

Abbasi, Seyed Mohammad Mehdi; Jalali, Ahvand

doi:10.1016/j.isatra.2019.07.028

Cited by 30 publications

(23 citation statements)

References 15 publications

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“…The equality of two fuzzy numbers is expressed as [18, 19]: Let

\overset{u}{true}, \overset{v}{true} \in E_{1}

;

\overset{u}{true}

is said to be equal to

\overset{v}{true}

iff

H ((), \overset{true~}{u}) = H ((), \overset{true~}{v})

\forall α_{u} = α_{v} \in ([], 0, 1)

. Similar to the definition of a fuzzy number, a fuzzy matrix,

\overset{A}{true} = {[{\overset{true~}{a}}_{pq}]}_{n \times n}

p, q = 1, \dots, n

, is defined as a matrix in which each of its components is a fuzzy number [20]. The inverse of a fuzzy matrix

\overset{A}{true}

is also considered as a matrix with fuzzy components for which the equality

H ((), {\overset{A}{true}}^{- 1}) H ((), \overset{true~}{A}) = I

holds where

I

is the identity matrix [20].…”

Section: Basic Conceptsmentioning

confidence: 99%

Fuzzy consensus of multi‐agent systems with granular fuzzy uncertainty in communication topology

Abdollahipour

Khandani

Jalali

2022

Asian Journal of Control

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In this paper, the consensus problem in linear multi‐agent systems with uncertain topology is investigated. The uncertainty in the communication topology is represented by granular fuzzy numbers obtained from expert knowledge, and the required calculations are performed with multidimensional relative–distance–measurement interval arithmetic. The concept of granular fuzzy graph and fuzzy Gershgorin disc theorem is introduced. Then a fuzzy consensus protocol is proposed for the multi‐agent system with fuzzy granular uncertain topology. A two‐step algorithm is also proposed to build the consensus protocol. We also propose a theorem for calculating the final value of fuzzy consensus, which shows the final value of consensus as a fuzzy number. Simulation results show the efficiency of the suggested algorithm.

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“…The equality of two fuzzy numbers is expressed as [18, 19]: Let

\overset{u}{true}, \overset{v}{true} \in E_{1}

;

\overset{u}{true}

is said to be equal to

\overset{v}{true}

iff

H ((), \overset{true~}{u}) = H ((), \overset{true~}{v})

\forall α_{u} = α_{v} \in ([], 0, 1)

. Similar to the definition of a fuzzy number, a fuzzy matrix,

\overset{A}{true} = {[{\overset{true~}{a}}_{pq}]}_{n \times n}

p, q = 1, \dots, n

, is defined as a matrix in which each of its components is a fuzzy number [20]. The inverse of a fuzzy matrix

\overset{A}{true}

is also considered as a matrix with fuzzy components for which the equality

H ((), {\overset{A}{true}}^{- 1}) H ((), \overset{true~}{A}) = I

holds where

I

is the identity matrix [20].…”

Section: Basic Conceptsmentioning

confidence: 99%

Fuzzy consensus of multi‐agent systems with granular fuzzy uncertainty in communication topology

Abdollahipour

Khandani

Jalali

2022

Asian Journal of Control

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“…A deep analysis of the stability of fuzzy linear dynamical systems under the notion of gr-differentiability has been reported in [102]. The performance criteria of second-order fuzzy linear dynamical systems and fuzzy tracking control of fuzzy linear dynamical systems under the concept of gr-differentiability have been investigated, respectively, in [95], [101]. By the aid of gr-Caputo derivative concept, the fuzzy fractional quadratic regulator problem was studied in [94] where a fuzzy feedback control was designed.…”

Section: Applications Of Fdesmentioning

confidence: 99%

A Review on Fuzzy Differential Equations

Mazandarani¹,

Li²

2021

IEEE Access

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Since the term "Fuzzy differential equations" (FDEs) emerged in the literature in 1978, prevailing research effort has been dedicated not only to the development of the concepts concerning the topic, but also to its potential applications. This paper presents a chronological survey on fuzzy differential equations of integer and fractional orders. Attention is concentrated on the FDEs in which a definition of fuzzy derivative of a fuzzy number-valued function has been taken into account. The chronological rationale behind considering FDEs under each concept of fuzzy derivative is highlighted. The pros and cons of each approach dealing with FDEs are also discussed. Moreover, some of the proposed FDEs applications and methods for solving them are investigated. Finally, some of the future perspectives and challenges of fuzzy differential equations are discussed based on our personal view point.

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“…Es un método de computación flexible que le ayuda a un computador a ordenar información del mundo real en una escala infinita acotada por los valores falso y verdadero; proporciona un soporte matemático formal al sostenimiento basado en el lenguaje natural, caracterizado por tratar de un razonamiento de tipo aproximado que hace uso de proposiciones que expresan información de carácter impreciso (5).…”

Section: Lógica Difusaunclassified

Controlador difuso para el cálculo del confort atmosférico en un invernadero

Casayco

Hidalgo

Quise

et al. 2018

Ing.

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The following research involves the manufacture of a diffuse controller for monitoring atmospheric comfort in a greenhouse. The comfort in a greenhouse is defined by: the temperature that varies from 20 °C to 25 °C and the relative humidity is around 50 %. The control and monitoring of these parameters is necessary for optimal microclimate formation in a greenhouse. The calculation of the temperature and relative humidity that helps us predict comfort is performed, by implementing a soft sensor using fuzzy logic. The objective of this research is to demonstrate efficiency for the automation and monitoring of artificial intelligence processes, in this case «fuzzy logic» that is based on the user's experience. In this investigation, basic electronics, programming and intermediate knowledge in fuzzy logic were applied. All this made possible the development of the controller.

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Fuzzy tracking control of fuzzy linear dynamical systems

Cited by 30 publications

References 15 publications

Fuzzy consensus of multi‐agent systems with granular fuzzy uncertainty in communication topology

Fuzzy consensus of multi‐agent systems with granular fuzzy uncertainty in communication topology

A Review on Fuzzy Differential Equations

Controlador difuso para el cálculo del confort atmosférico en un invernadero

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