Consensus Of Fractional-order Multi-agent Systems Research Articles

Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

This paper is devoted to the consensus problems for a fractional-order multiagent system (FOMAS) with double integral and time delay, the dynamics of which are double-integrator fractional-order model, where there are two state variables in each agent. The consensus problems are investigated for two types of the double-integrator FOMAS with time delay: the double-integrator FOMAS with time delay whose network topology is undirected topology and the double-integrator FOMAS with time delay whose network topology is directed topology with a spanning tree in this paper. Based on graph theory, Laplace transform, and frequency-domain theory of the fractional-order operator, two maximum tolerable delays are obtained to ensure that the two types of the double-integrator FOMAS with time delay can asymptotically reach consensus. Furthermore, it is proven that the results are also suitable for integer-order dynamical model. Finally, the relationship between the speed of convergence and time delay is revealed, and simulation results are presented as a proof of concept.

Consensus of Fractional-Order Multiagent Systems with Nonuniform Time Delays

Due to the complex external environment, many multiagent systems cannot be precisely described or even cannot be described by an integer-order dynamical model and can only be described by a fractional-order dynamical model. In this paper, consensus problems are investigated for two types of fractional-order multiagent systems (FOMASs) with nonuniform time delays: FOMAS with symmetric time delays and undirected topology and FOMAS with asymmetric time delays and directed topology. Employing the Laplace transform and the frequency-domain theory, two delay margins are obtained to guarantee the consensus for the two types of FOMAS, respectively. These results are also suitable for the integer-order dynamical model. Finally, simulation results are provided to illustrate the effectiveness of our theoretical results.

Necessary and Sufficient Conditions for Consensus of Fractional-Order Multiagent Systems via Sampled-Data Control.

In this paper, the consensus of fractional-order multiagent systems (FOMASs) is considered via sampled-data control over directed communication topology with the order 0 <; α <; 1. Two cases are considered. One is FOMASs without leader, and the other is FOMASs with a leader. For each case, by applying matrix theory and algebraic graph theory, some algebraic-type necessary and sufficient conditions based on the sampling period, the fractional-order, the coupling gain, and the structure of the network are established for achieving consensus of the system. Moreover, for the network with a dynamic leader, the sampling period, the coupling gain, and the spectrum of the Laplacian matrix are carefully devised, respectively. Finally, several simulation examples are employed to validate the effectiveness of the theoretical results.

Consensus of Fractional-Order Multi-Agent Systems with Input Time Delay

AbstractMany phenomena in inter-disciplinary fields can be explained naturally by coordinated behavior of agents with fractional-order dynamics. Under the assumption that the interconnection topology of all agents has a spanning tree, the consensuses of linear and nonlinear fractional-order multi-agent systems with input time delay are studied, respectively. Based on the properties of Mittag-Leffler function, matrix theory, stability theory of fractional-order differential equations, some sufficient conditions on consensus are derived by using the technique of inequality, which shows that the consensus can be achieved for any bounded input time delay. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.

Consensus of Fractional-Order Multiagent Systems with Double Integrator under Switching Topologies

Due to the complexity of the practical environments, many systems can only be described with the fractional-order dynamics. In this paper, the consensus of fractional-order multiagent systems with double integrator under switching topologies is investigated. By applying Mittag-Leffler function, Laplace transform, and dwell time technique, a sufficient condition on consensus is obtained. Finally, a numerical simulation is presented to illustrate the effectiveness of the theoretical result.

Consensus of fractional-order multi-agent systems with linear models via observer-type protocol

In this paper, the consensus of fractional-order multi-agent systems with general linear models is investigated , where the fractional-order α satisfies 0<α≤n for any given natural number n. A distributed observer-type protocol is proposed. By applying the fractional-order stability theory, properties of the Kronecker product, Mittag-Leffler function and Laplace transform, a sufficient condition is obtained under the assumption that each agent is stabilizable and detectable. Finally, a numerical simulation is presented to illustrate the usefulness of the theoretical result, which shows that the result obtained in this paper generalizes and improves some existing results in literature.

Consensus with a reference state for fractional-order multi-agent systems

This paper investigates consensus of fractional-order multi-agent systems (MASs) with a reference state. First, a consensus control law with a constant reference state is given using graph theory and stability analysis of fractional-order. Then, a general control law and a particular one for consensus of fractional-order MASs with a time-varying reference state are proposed. Next, the above control laws are extended to solve formation tracking problem. Finally, several simulations are presented to verify the effectiveness of the obtained results.

Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control

In this paper, the leader-following consensus problem of fractional-order multi-agent systems is considered via adaptive pinning control. The dynamics of leader and all followers with linear and nonlinear functions are investigated, respectively. We assume that the node should be pinned if its in-degree is less than its out-degree in the paper. Under this assumption and based on the stability theory of fractional-order differential systems, some leader-following consensus criteria are derived, which are easily obtained by matrix inequalities. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and the Riccati inequality. Several simulation examples are presented to demonstrate the effectiveness of the proposed method.

Robust consensus of fractional-order multi-agent systems with positive real uncertainty via second-order neighbors information

This paper addresses the robust consensus problem of fractional-order linear multi-agent systems with positive real uncertainty where the fractional-order α satisfies 0<α<2. For multi-agent systems with fixed undirected topology, a distributed protocol is proposed based on the information of second-order neighbors. Then, new LMI-based sufficient conditions for robust consensus of fractional-order multi-agent systems are obtained and the feedback matrix is also determined accordingly. Finally, numerical simulation examples are presented to demonstrate the effectiveness of the proposed approach.

Leader-following consensus of fractional-order multi-agent systems under fixed topology

The leader-following consensus problem of fractional-order multi-agent systems is considered. In the system, the dynamics of each agent and leader are nonlinear systems. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and Lyapunov method. Several simulation examples are presented as a proof of concept.