Abstract
A leader-following consensus for Caputo fractional multi-agent systems with nonlinear intrinsic dynamics is investigated. The second Lyapunov method is used to design a control protocol ensuring a consensus for two types of multi-agent systems. Contrary to the previous studies on leader-following consensus, the investigation covers systems with bounded and unbounded time-dependent Lipschitz coefficients in the intrinsic dynamics. Moreover, coupling strength describing the interactions between agents is considered to be a function of time.
Highlights
1 Introduction A canonical problem that appears in the coordination of dynamic multi-agent networks is the consensus problem: given initial values of nodes, establish conditions under which, through local interactions and computations, nodes asymptotically reach an agreement upon a common state
The consensus problem plays an important role in various contexts such as wireless communication networks, sensor networks, leader election, clock phase synchronization, and air traffic control systems
Fractional calculus is a generalization of differentiation and integration to the arbitrary order
Summary
A canonical problem that appears in the coordination of dynamic multi-agent networks is the consensus problem: given initial values of nodes (agents), establish conditions under which, through local interactions and computations, nodes (agents) asymptotically reach an agreement upon a common state. This paper is concerned with the last-mentioned case of systems, that is, we study a leader-following consensus for fractional multi-agent systems. Theorem 1 concerns the case of multi-agent systems with intrinsic nonlinear dynamics described by a function with a bounded time-dependent Lipschitz coefficient and time-varying coefficients in the control protocol.
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