Consensus of Uncertain Linear Multi-agent Systems with Granular Fuzzy Dynamics

Abdollahipour, Razie; Khandani, Khosro; Jalali, Ali

doi:10.1007/s40815-021-01237-0

Cited by 12 publications

(3 citation statements)

References 37 publications

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“…In [25,26] , under the concept of granular differentiation, the fuzzy optimization problems with the general fuzzy function as the objective function for type-1 and type-2 fuzzy functions have been investigated. On the basis of the powerful notion of granular derivative, the consensus problem for linear multi-agent systems with granular fuzzy uncertainty has been investigated in [27,28] . In [29] , the stability and controllability of fuzzy singular dynamical systems under the concept of granular calculus has been studied.…”

Section: Some Of the Applications Of Granular Derivativementioning

confidence: 99%

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Abbasi¹,

Jalali²

2023

Fuzzy Information and Engineering

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In this work, the tracking control of a class of uncertain linear dynamical systems is investigated. The uncertainty is considered to be represented as fuzzy numbers, and hence, these uncertain dynamical systems are referred to as fuzzy linear dynamical systems, which are presented in the form of fuzzy differential equations (FDEs). The solution of an FDE is found using an approach called relative-distance-measure fuzzy interval arithmetic and under the granular differentiability concept. The control objective is to provide a control law such that the output of the system tracks a desired reference input in the presence of uncertainties. To this end, a theorem is proposed, which suggests that the control law should take the form of a feedback of fuzzy states with fuzzy gains and a fuzzy pre-compensator. However, since the fuzzy states of the system may not always be measurable, a fuzzy observer is designed for the estimation of such fuzzy states. It is also clearly shown that the generalized Hukuhara differentiability concept is unable for solving the problem examined in this study. Finally, the efficiency of the approach is examined for a plane landing control problem.

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Section: Some Of the Applications Of Granular Derivativementioning

confidence: 99%

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Abbasi¹,

Jalali²

2023

Fuzzy Information and Engineering

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“…Most of the results in cooperative control of MASs have assumed integer-order dynamics for all of the agents. [10][11][12] Fractional MASs have attracted considerable attention in recent years. This is motivated by the fact that the agents working in complex environments are best modeled by fractional-order dynamics.…”

Section: Introductionmentioning

confidence: 99%

Formation tracking control of fractional-order multi-agent systems with fixed-time convergence

Zamani

Majd

Khandani

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this article, the fixed-time formation problem in fractional-order multi-agent systems is addressed. By using the Reimann–Liouville fractional derivative, the memory effects are considered in the dynamics of agents. The goal is to design distributed controllers for such agents of fractional order to achieve formation with a fixed-time convergence rate. To solve this problem, a fractional-order control protocol with a neighborhood-based error variable is proposed. By using the fixed-time Lyapunov stability theorem, it has been theoretically shown that the fixed-time formation tracking can be achieved within a certain settling time, and the upper bound of the settling time has been obtained explicitly. The proposed upper bound does not depend on the initial conditions. Finally, several simulations are worked out to verify the theoretical results. The superiority of the proposed method over finite-time protocols has been illustrated.

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“…The consensus protocol for a class of MASs has been presented in Rezaee et al [10] for the case where the presence or absence of communication graph edges is stochastic. Abdollahipour et al [11] distributed consensus problem for multi‐agent systems with fuzzy uncertainty is considered. Although the uncertainty is considered to be in agents' dynamics.…”

Section: Introductionmentioning

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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Consensus of Uncertain Linear Multi-agent Systems with Granular Fuzzy Dynamics

Cited by 12 publications

References 37 publications

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Formation tracking control of fractional-order multi-agent systems with fixed-time convergence

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

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