Leader-Following Consensus of Fractional Nonlinear Multiagent Systems

Abstract

The leader-following consensus of fractional nonlinear multiagent systems is investigated over an undirected fixed interaction graph. Mittag-Leffler stability and the fractional Lyapunov direct method are firstly introduced into the fractional multiagent systems. The sufficient conditions are given to guarantee that the leader-following consensus can be achieved in the systems with both single-integrator dynamics and double-integrator dynamics. Finally, the numerical simulations are given to verify the correctness of the presented theory.

Discrete leader‐following consensus

“…In the literature, many different consensus algorithms have been proposed; we can mention here those based on nearest-neighbor rules, 3,[8][9][10][11][12] bounded confidence, [13][14][15][16] or a virtual leader. [17][18][19] The virtual leader is a special agent whose motion is independent of all the other agents and thus is followed by all the other ones. Such a problem is commonly called leader-following consensus problem.…”

Consensus Analysis of Fractional-Order Multiagent Systems with Double-Integrator

“…Simulation comparison with some existing protocols in literature is done, which shows the effectiveness of the Theorem 8. For the sake of comparison, we restate the control protocol without leader in [19] as follows:…”

“…In [18], the authors discussed the consensus of fractional-order heterogeneous multiagent systems by the Kronecker product technique, the fractional-order stability theory, and LMIs. In [19], the Mittag-Leffler stability and the fractional Lyapunov direct method were firstly introduced into the fractional multiagent systems. Sufficient conditions were given to guarantee that the leader-following consensus can be achieved with both single-integrator dynamics and double-integrator dynamics, respectively.…”

Non-invasive Control of the Fractional Hegselmann–Krause Type Model

“…positions, velocity, opinion) by interacting with their neighbours. Consensus algorithms are based on nearest-neighbour rules [6,7,10,21], bounded confidence [4,8,9,20] or a virtual leader [3,23,28]. The virtual leader is an agent whose motion is independent of all the other agents, and thus is followed by all the other ones.…”