Synchronization of linear systems via relative actuation

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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“…Remark The solvability of LMI

italicAP + P A^{T} - 2 B B^{T} < 0

is equal to the equation

A^{T} Q + italicQA + I - italicQB B^{T} Q = 0

, and the feedback gain matrix can be selected as

K = - B^{T} Q

([21, 22]).…”

Section: Fuzzy Consensus Problem and Fuzzy Consensus Protocol Designmentioning

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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“…According to Lemma 1 , all the eigenvalues of L j ω (τ ) will be larger than or equal to β. Hence, when α satisfies (13) , by Lemma 4 in the appendix, there exists an ε * such that for any ε ∈ (0, ε * ], the matrix (15) has no eigenvalues on the imaginary axis. As noted before, this implies that the closed-loop system ( 12) is asymptotically stable for any communication delay τ i j ∈ R + .…”

Section: Undirected Graphsmentioning

confidence: 99%

“…In the past few decades, synchronization problems for multiagent systems have received substantial attention, where the objective is to achieve asymptotic agreement on a common state ( state synchronization ) or output trajectory ( output synchronization ) among agents of the network through decentralized control protocols. Some early results can be found in, e.g., [4,9,11,15] , for state synchronization problems of homogeneous networks (i.e. agents are identical), and in, e.g., [1,3,18,20,21] , for output synchronization problems for heterogeneous networks.…”

Section: Introductionmentioning

confidence: 99%

Synchronization in the presence of unknown, nonuniform and arbitrarily large communication delay

Zhang

Saberi

Stoorvogel

2017

European Journal of Control

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“…Given that it is impractical for each follower to access the leader's information directly for controller design, one of the primary challenges of addressing this problem is to devise a distributed controller for every follower that employs its own information as well as that of its neighbors. [14]- [16]. A common way to overcome this challenge, as is mentioned in [17]- [20], is to design an adaptive distributed observer for Beining Wu (Corresponding author) is with the Department of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, China (e-mail: wbn@ahnu.edu.cn;).…”

Section: Introductionmentioning

confidence: 99%

Model-Free Cooperative Optimal Output Regulation for Linear Discrete-Time Multi-Agent Systems Using Reinforcement Learning

2023

Preprint

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In this paper, an off-policy model-free algorithm is presented for solving the cooperative optimal output regulation problem for linear discrete-time multi-agent systems. First, an adaptive distributed observer is designed for each follower to estimate the leader's information. Then, a distributed feedback-feedforward controller is developed for each follower to solve the cooperative optimal output regulation problem utilizing the follower's state information and the adaptive distributed observer. Based on reinforcement learning method, an adaptive algorithm is presented to find the optimal feedback gains via online data collecting from system trajectory. By designing a Sylvester map, the solution to the regulator equations is calculated via data collected from the optimal feedback gain design steps, and the feedforward control gain is found. Finally, an off-policy model-free algorithm is proposed to design the distributed feedback-feedforward controller for each follower to solve the cooperative optimal output regulation problem. A numerical example is given to verify the effectiveness of this proposed approach.

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Synchronization of linear systems via relative actuation

Abstract: Synchronization in networks of discrete-time linear time-invariant systems is considered under relative actuation. Neither input nor output matrices are assumed to be commensurable. A distributed algorithm that ensures synchronization via dynamic relative output feedback is presented.

Cited by 9 publications

References 17 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

Synchronization in the presence of unknown, nonuniform and arbitrarily large communication delay

Model-Free Cooperative Optimal Output Regulation for Linear Discrete-Time Multi-Agent Systems Using Reinforcement Learning

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