Consensus Of Fractional-order Multi-agent Systems Research Articles

Leader-Following Output Feedback H∞ Consensus of Fractional-Order Multi-Agent Systems with Input Saturation

This paper investigates the leader-following H∞ consensus of fractional-order multi-agent systems (FOMASs) under input saturation via the output feedback. Based on the bounded real lemma for FOSs, the sufficient conditions of H∞ consensus for FOMASs are provided in α∈0,1 and 1,2, respectively. Furthermore, the iterative linear matrix inequalities (ILMIs) approaches are applied for solving quadratic matrix inequalities (QMIs). The ILMI algorithms show a method to derive initial values and transform QMIs into LMIs. Mathematical tools are employed to transform the input saturation issue into optimal solutions of LMIs for estimating stable regions. The ILMI algorithms avoid the conditional constraints on matrix variables during the LMIs’ construction and reduce conservatism. The approach does not disassemble the entire MASs by transformations to the Laplacian matrix, instead adopting a holistic analytical perspective to obtain gain matrices. Finally, numerical examples are conducted to validate the efficiency of the approach.

Boundary Control Strategies for Consensus of Fractional-Order Multi-Agent Systems Based on Coupling PDE-ODEs

Boundary Control Strategies for Consensus of Fractional-Order Multi-Agent Systems Based on Coupling PDE-ODEs

Composite adaptive fuzzy bipartite consensus of fractional-order multiagent systems with a switched event-triggered mechanism

This paper focuses on online recorded-data-based composite adaptive fuzzy bipartite consensus control for uncertain fractional-order multiagent systems with interconnected terms and external disturbances by employing a switched-threshold-based event-triggered mechanism (ETM) under the backstepping structure. Fuzzy logic system is used as a universal function approximation to deal with function uncertainties that are not prone to model in the system. A new composite learning adaptive parameter design scheme that synthesizes both prediction error and tracking error is developed to enhance the tracking performance, where the prediction error is raised from the utilization of online recorded data and instantaneous data. A unique switched-threshold-based ETM is introduced, in which the information transmission between the sensor and the controller is imposed on one of the individuals. One merit of this work consists in that it can automatically and rapidly switch and adjust between the fixed threshold and relative threshold ETM according to the amplitude of input signals to balance the network resources and impede the occurrence of pulse phenomenon. In addition, it is theoretically proven that the proposed scheme can ensure that all internal signals of the closed-loop system are bounded and achieve local bipartite consistent errors through the fractional Lyapunov stability criterion. Finally, a numerical example is provided to confirm the feasibility of the proposed approach.

Positive Consensus of Fractional-Order Multiagent Systems Over Directed Graphs.

This article investigates the positive consensus problem of a special kind of interconnected positive systems over directed graphs. They are composed of multiple fractional-order continuous-time positive linear systems. Unlike most existing works in the literature, we study this problem for the first time, in which the communication topology of agents is described by a directed graph containing a spanning tree. This is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains, which renders the positivity analysis fairly challenging. Based on the existing results in spectral graph theory, fractional-order systems (FOSs) theory, and positive systems theory, we derive several necessary and/or sufficient conditions on the positive consensus of fractional-order multiagent systems (PCFMAS). It is shown that the protocol, which is designed for a specific graph, can solve the positive consensus problem of agents over an additional set of directed graphs. Finally, a comprehensive comparison study of different approaches is carried out, which shows that the proposed approaches have advantages over the existing ones.

Consensus of fractional-order multi-agent systems with sampled position data

In this paper, the consensus of fractional-order multi-agent systems with the order α satisfying α∈(0,1] is investigated. A novel distributed control protocol is constructed, in which only the past sampled position data of neighbors are utilized. Then, based on Laplace transform, Mittag-Leffler function, and matrix theory, necessary and sufficient criteria depending on the order, coupling gains, sampling period, and communication topology, are established to attain consensus for the systems. Meanwhile, the intervals of coupling gains and sampling period associated with the maximum eigenvalue of Laplacian matrix over an undirected graph are presented to attain consensus. Finally, the availability of theoretical results is verified by numerical simulations.

Consensus of fractional-order multi-agent systems via event-triggered pinning impulsive control

In this paper, the consensus of fractional-order multi-agent systems is studied. By utilizing the unique properties of fractional-order calculus, namely hereditary and infinite memory, a new design scheme of the event-triggered pinning impulsive control strategy is proposed. Compared with the fixed pinning technique, the pinning agents here can be variable at each impulsive instant based on the considered two pinning rules (i.e., selecting randomly and according to the distances of error states). With the introduced rules, sufficient conditions are derived for consensus of systems, and the Zeno behavior is also excluded. Finally, our results show that the distance-ordered pinning can be achieved faster than the one with randomly pinning selection, and the inner impulsive gain of the impulsive controller can not be too large.

Consensus of fractional-order multi-agent systems via current and time-delay states feedback

The consensus problems of fractional-order multi-agent systems(FOMAS) are investigated under a fixed interaction graph. A consensus protocol that has current and time-delay states is designed. The conception of practical consensus of FOMAS is proposed. The asymptotical consensus condition is obtained by taking advantage of Laplace transform. Furthermore, the practical consensus condition of the FOMAS with the protocol is given by direct derivation. Through numerical simulation, we find that the standard control protocol can not achieve consensus in some situations. However, the proposed protocol could make the states of multi-agent be consensus or even practical consensus.

State-based event-triggered consensus strategy for Takagi–Sugeno fuzzy fractional-order multiagent systems with switching topologies

This article addresses the event-triggered consensus problem for Takagi–Sugeno fuzzy fractional-order multiagent systems with switching topologies. First, to effectively avoid the frequent communication among agents, a state-based event-triggered consensus strategy is designed, which uses the local information from neighboring agents at sampling moments. Then, several sufficient conditions, which rely on the fractional derivative number and time delay information, are presented to guarantee the consensus of fractional-order multiagent systems based on Takagi–Sugeno fuzzy model. Moreover, Zeno behaviors are precluded by proving that the interval length of the two consecutive event-triggering moments for each agent is greater than a positive constant. Finally, some numerical examples are presented, which not only demonstrated the rationality of our proposed consensus protocol but also shown that the presented consensus method based on the designed event-triggered control protocol has the advantage for avoiding communication congestion compared to the existing results.

Positive consensus of fractional-order multi-agent systems

Positive consensus of fractional-order multi-agent systems

Cluster consensus of fractional-order non-linear multi-agent systems with switching topology and time-delays via impulsive control

In this paper, a cluster consensus problem for fractional-order nonlinear multi-agent systems with fixed and switching topologies and time delays is considered. The problem is solved in three cases: (i) fixed topology and time delays, (ii) switching topology, and (iii) switching topology and time delays. Cluster consensus is achieved for fractional-order multi-agent systems by using the impulsive control method. Cluster consensus algorithms are studied by using Mittag–Leffler stability and the fractional Lyapunov direct method and some sufficient conditions are obtained to achieve cluster consensus of fractional-order multi-agent systems with nonlinear dynamics under switching topologies and time delays. Finally, simulation results are presented to show the validity of the proposed control strategies.

Consensus of fractional-order multi-agent systems with uncertain topological structure: A Takagi-Sugeno fuzzy event-triggered control strategy

In this paper, the consensus problem of fractional-order multi-agent systems (FOMASs) with uncertain topological structure via designed Takagi-Sugeno fuzzy event-triggered control is investigated. First, Takagi-Sugeno fuzzy event-triggered control for FOMASs is designed to effectively alleviate the congestion of communication capacity. Then, by utilizing the tools including Lyapunov function method, the fractional inequality technique and Laplace transform, some sufficient conditions for the consensus of FOMASs with uncertain topological structure are obtained, and a rigorous proof is given to exclude Zeno behavior for the designed Takagi-Sugeno fuzzy event-triggered control. Finally, two examples are given to not only illustrate the availability of the proposed approach but also show that the designed Takagi-Sugeno fuzzy event-triggered control in this paper is more effective than the previous methods.

Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth

This paper considers the global leader-following consensus of fractional-order multi-agent systems (FMASs), where the inherent dynamics is modeled to be discontinuous, and subject to nonlinear growth. Firstly, based on convex functions, three formulas on fractional derivative are established respectively. By applying the proposed formulas, a principle of convergence in finite-time for absolutely continuous functions is developed. Secondly, a new nonlinear control protocol, which includes discontinuous factors, is designed. Under fractional differential inclusion framework, by means of Lyapunov functional approach and Clarke’s non-smooth analysis technique, the sufficient conditions with respect to the global consensus are achieved. In addition, the setting time is explicitly evaluated for the global leader-following consensus in finite time. Finally, two illustrative examples are provided to check the correction of the obtained results in this paper.

Leader-following consensus of fractional-order multi-agent systems based on event-triggered control

In this paper, an efficient event-triggered control is designed to address the leader-following consensus problem for the fractional-order multi-agent systems. First, in order to reduce the conservation of consensus criteria, a novel Wirtinger-based fractional-order integral inequality is proposed. Second, an adaptive control is designed by using a new event-triggered scheme without Zeno behavior, which can effectively reduce the communication cost in network. Later in order to analyze the consensus of the fraction-order leader-following systems, we employ a new approach based on fractional Lyapunov direct method. Finally, combining Wirtinger-based fractional-order integral inequality, the event-triggered adaptive control as well as the proposed consensus method, the consensus criteria of the leader-following fractional-order multi-agent systems are obtained. Two numerical examples are used to test the effectiveness and feasibility of the results presented in this study.

Asymptotical consensus of fractional-order multi-agent systems with current and delay states

In this paper, we study some new fractional-order multi-agent systems with current and delay states (FMASCD). Using the generalized Nyquist’s stability criterion and Gerschgorin’s circle theorem, we obtain the bounded input-bounded output (BIBO) stability and asymptotical consensus of the FMASCD under mild conditions. Moreover, we give some numerical examples to illustrate our main results.

Consensus in Fractional-Order Multi-Agent Systems With Intermittence Sampled Data Over Directed Networks

The leaderless consensus of fractional-order multi-agent systems (FOMASs) by intermittence sampled data control method is investigated in this brief, for which a distributed intermittence sampled data control protocol is presented to reduce the updating rate and working time of controllers. Subsequently, the Laplace transform and the stability theory are utilized to derive some necessary and sufficient consensus criteria that show the relations among the fractional order, sampling period, communication width, coupling strengths, and network topology. What is more, it can be discovered that both the communication width and sampling period have the lower and upper bounds for given networks to attain leaderless consensus. Finally, a numerical simulation example is presented to prove the theoretical results.

Neuro-adaptive leaderless consensus of fractional-order multi-agent systems

Leaderless consensus control problem of fractional-order multi-agent systems (FOMASs) with unknown nonlinearities and unknown external disturbances is investigated in this paper. Firstly, based on neural networks, an adaptive control protocol with integer-order dynamics is proposed to approximate the unknown nonlinearities, which is easy to implement in reality. And then, a novel auxiliary Lyapunov function which contains Riemman–Liouvile fractional-order integral is first constructed to verify the effectiveness of the designed control protocol. Moreover, the convergence analysis of FOMASs is finished by taking the Barbalat lemma for the first time. Finally, theoretical results are demonstrated by several numerical simulations.

Consensus of fractional-order multi-agent systems with impulsive disturbance

The consensus problem of fractional-order multi-agent systems (MASs) with impulsive disturbance is investigated in this paper. Based on the theory of fractional order system and Lyapunov stability, some sufficient conditions are derived to ensure the consensus of MASs with impulsive disturbance. Comparing with the existing results, the method proposed in this paper is more applicable. Finally, simulation results verify the correctness and effectiveness of the main results.

Consensus of Multi-Integral Fractional-Order Multiagent Systems with Nonuniform Time-Delays

Consensus of fractional-order multiagent systems (FOMASs) with single integral has been wildly studied. However, the dynamics with multiple integral (especially double integral to sextuple integral) also exist in FOMASs, and they are rarely studied at present. In this paper, consensus problems for multi-integral fractional-order multiagent systems (MIFOMASs) with nonuniform time-delays are addressed. The consensus conditions for MIFOMASs are obtained by a novel frequency-domain method which properly eliminates consensus problems of the systems associated with nonuniform time-delays. Besides, the method revealed in this paper is applicable to classical high-order multiagent systems which is a special case of MIFOMASs. Finally, several numerical simulations with different parameters are performed to validate the correctness of the results.

Robust consensus of fractional-order multi-agent systems with input saturation and external disturbances

Abstract In this paper, the robust consensus problem of fractional-order multi-agent systems with input saturation and external disturbances is studied under a directed fixed topology. It’s the first time to consider the fractional-order agent subject to input saturation. When there exist input saturation and external disturbances simultaneously, by means of the Mittag–Leffler stability theorem and low gain feedback technique, a control protocol is presented to guarantee the robust consensus can be achieved. Moreover, as a special case, the leader-following consensus can be achieved when there only exists input saturation. Finally, the results are verified by several simulation examples.

Consensus of fractional-order multiagent system via sampled-data event-triggered control

This paper investigates the consensus of fractional-order multiagent systems via sampled-data event-triggered control. Firstly, an event-triggered algorithm is defined using sampled states. Thus, Zeno behaviors can be naturally avoided. Then, a distributed control protocol is proposed to ensure the consensus of fractional-order multiagent systems, where each agent updates its current state based on its neighbors’ states at event-triggered instants. Furthermore, the pinning control technology is taken into account to ensure all agents in multiagent systems reach the specified reference state. With the aid of linear matrix inequalities (LMI), some sufficient conditions are obtained to guarantee the consensus of fractional-order multiagent system. Finally, numerical simulations are presented to demonstrate the theoretical analysis.