Consensus of One-Sided Lipschitz Multiagents Under Switching Topologies

Razaq, Muhammad Ahsan; Rehan, Muhammad; Ahn, Choon Ki; Khan, Abdul Qayyum; Tufail, Muhammad

doi:10.1109/tsmc.2019.2897775

Cited by 26 publications

(36 citation statements)

References 37 publications

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“…The symbols

x_{i} ()(, t) \in R^{n},

u_{i} ()(, t) \in R^{p},

and

ω_{i} ()(, t) \in L_{2}^{q} ()[, 0, normal∞)

are state vector, control input, and

L_{2}

norm‐bounded external disturbance for followers which means that the energy of the disturbance signal

ω_{i} ()(, t)

is bounded.

f ()(, x_{i} ()(, t), t)

represents the non‐linearity that satisfies the following Assumptions 1 and 2 [7–10, 16–18]: Assumption 1 For

z, \overset{false¯}{z} \in R^{n},

let the inequality

(⟩⟨, f ()(, z, t) - f ()(, \overset{false¯}{z}, t), z - \overset{false¯}{z}) \leq ρ {∥z - \bar{z}∥}_{2}^{2}

holds with OSL constant

ρ \in double-struckR

. Assumption 2 [7–10, 16–18] : For

z, \overset{false¯}{z} \in R^{n},

suppose that

\begin{matrix} right leftthickmathspace.5em \\ {(∥∥, f ()(, z, t) - f ()(, \overset{false¯}{z}, t))}_{2}^{2} \\ \leq ε (∥∥, z -) \end{matrix}

…”

Section: System Descriptionmentioning

confidence: 99%

“…For switching communication graphs, the problem of consensus control of OSL agents using observers and by considering intermitted communications has been posed in [17]. This work is extended for addressing the conservatism in OSL non‐linearity handling under switching topologies in [18], but the issue of multiple Lyapunov functions (MLFs) for achieving less conservative controllers is not realised in the study. The MLFs approach is applied for consensus of MASs in [19, 20].…”

Section: Introductionmentioning

confidence: 99%

“…Another framework for dealing with the consensus of generalised linear incremental form of systems is addressed in [21]; however, the study has a limitation in working out with the computation of controller parameters. The conventional works [14, 15] and [17–21] on linear, Lipschitz, and OSL systems for dealing with the switching topologies do not incorporate external disturbances, and consensus control of non‐linear systems over switching graphs under perturbations is a non‐trivial research problem. In addition, these works ([8, 14–18, 20, 21]) assume zero input to the leader, however, leaders can be derived through an external input.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast to conventional dwell‐time constraint, ADT has less limitations on the switching signal and it can consider a random signal [32]. For dealing with the non‐zero input at the leader, an extra term is applied to the consensus protocol, and the resultant conditions for the consensus controller synthesis are strived in contrast to [7–10, 16–18, 20, 21]. This additional term assures robust consensus between OSL agents in the presence of bounded signal to the leader agent without loss of generality.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

H∞ leader‐based consensus of non‐linear multi‐agents over switching graphs and disturbances using multiple Lyapunov functions

Razaq

Rehan

Tahir

et al. 2020

IET Control Theory & Appl

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This study deals with the multiple Lyapunov functions approach for the robust leader‐following consensus of one‐sided Lipschitz (OSL) multiagents, connected via switching topologies under external disturbances. Disturbances have been accounted for followers, connected via a directed graph with a spanning tree from the leader root. The authors stipulate two consensus protocols, based on the absence or existence of norm‐bounded reference input to the leader, and provide matrix inequalities for designing the parameters of consensus controllers. In the presence of L2 bounded disturbances, the proposed protocol ensures H∞ consensus criterion for minimisation of the effect of disturbances to the consensus error between the leader and followers. A remedy for striking robustness against external perturbations has been provided in the present work in contrast to the conventional consensus schemes on OSL agents. Switching OSL mobile agents and aircraft carriers consisting of a leader and five followers have been simulated in the existence of reference input and disturbances to demonstrate the empirical proficiency of the consensus protocol schemes.

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“…The symbols

x_{i} ()(, t) \in R^{n},

u_{i} ()(, t) \in R^{p},

and

ω_{i} ()(, t) \in L_{2}^{q} ()[, 0, normal∞)

are state vector, control input, and

L_{2}

norm‐bounded external disturbance for followers which means that the energy of the disturbance signal

ω_{i} ()(, t)

is bounded.

f ()(, x_{i} ()(, t), t)

represents the non‐linearity that satisfies the following Assumptions 1 and 2 [7–10, 16–18]: Assumption 1 For

z, \overset{false¯}{z} \in R^{n},

let the inequality

(⟩⟨, f ()(, z, t) - f ()(, \overset{false¯}{z}, t), z - \overset{false¯}{z}) \leq ρ {∥z - \bar{z}∥}_{2}^{2}

holds with OSL constant

ρ \in double-struckR

. Assumption 2 [7–10, 16–18] : For

z, \overset{false¯}{z} \in R^{n},

suppose that

\begin{matrix} right leftthickmathspace.5em \\ {(∥∥, f ()(, z, t) - f ()(, \overset{false¯}{z}, t))}_{2}^{2} \\ \leq ε (∥∥, z -) \end{matrix}

…”

Section: System Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

H∞ leader‐based consensus of non‐linear multi‐agents over switching graphs and disturbances using multiple Lyapunov functions

Razaq

Rehan

Tahir

et al. 2020

IET Control Theory & Appl

Self Cite

View full text Add to dashboard Cite

show abstract

“…In practical application, the communication link failures and the establishment of new link lead to frequent changes in the communication topology among agents due to communication equipment faults and disturbances. To name a few, in [22], the consensus tracking problems are considered for one-sided Lipschitz MASs under switching topologies. The consensus tracking is investigated for Lipschitz MASs under switching directed topologies in [23].…”

Section: Introductionmentioning

confidence: 99%

Guaranteed Cost Consensus for Fuzzy Multi-Agent Systems With Switching Topologies

Xing

et al. 2020

IEEE Access

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This paper concentrates on guaranteed cost consensus problem for nonlinear multi-agent systems (MASs) under directed switching topologies. First, a novel polynomial fuzzy model is constructed for describing the nonlinear error MASs that are formulated by follower agents and a leader agent. Then, a consensus tracking protocol is devised to ensure that the MASs with changing topologies can achieve agreement. For the established fuzzy MASs, guaranteed cost function is introduced based on error states and control inputs. By the multiple polynomial Lyapunov function, we present relaxed sufficient condition to reach consensus with a guaranteed cost for the fuzzy MASs. Moreover, the designed consensus protocol can realize guaranteed cost by the upper bound for any initial error state. The obtained condition is converted to sum of squares and solved numerically. Finally, an example is given to illustrate the validity of the proposed consensus technique. INDEX TERMS Switching topology, multi-agent system, guaranteed cost, fuzzy modeling.

show abstract

Observer‐based leader‐following consensus of one‐sided Lipschitz multi‐agent systems over input saturation and directed graphs

Razaq

Rehan

Hussain

et al. 2023

Asian Journal of Control

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This paper investigates a local observer‐based leader‐following consensus control of one‐sided Lipschitz (OSL) multi‐agent systems (MASs) under input saturation. The proposed consensus control scheme has been formulated by using the OSL property, input saturation, directed graphs, estimated states, and quadratic inner‐boundedness condition by attaining the regional stability. It is assumed that the graph always includes a (directed) spanning tree with respect to the leader root to develop matrix inequalities for investigating parameters of the proposed observer and consensus protocols. Further, a new observer‐based consensus tracking method for MASs with saturation, concerning independent topologies for communicating outputs and estimates over the network, is explored to deal with a more perplexing and realistic situation. In contrast to the traditional methods, the proposed consensus approach considers output feedback and deals with the input saturation for a generalized class of nonlinear systems. The efficiency of the obtained results is illustrated via application to a group of five moving agents in the Cartesian coordinates.

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Consensus of One-Sided Lipschitz Multiagents Under Switching Topologies

Cited by 26 publications

References 37 publications

H∞ leader‐based consensus of non‐linear multi‐agents over switching graphs and disturbances using multiple Lyapunov functions

H∞ leader‐based consensus of non‐linear multi‐agents over switching graphs and disturbances using multiple Lyapunov functions

Guaranteed Cost Consensus for Fuzzy Multi-Agent Systems With Switching Topologies

Observer‐based leader‐following consensus of one‐sided Lipschitz multi‐agent systems over input saturation and directed graphs

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