Consensus Problem with a Reference State for Fractional‐Order Multi‐Agent Systems

Abstract

In this paper, the consensus problem of fractional‐order multi‐agent systems with a reference state is studied under fixed directed communication graph. At the beginning, the convergence speeds of fractional‐order multi‐agent systems are investigated based on the Mittag‐Leffler function. Then, a common consensus control law and a consensus control law based on error predictor are proposed, and it is shown that the consensus tracking can be achieved using the above control laws when a communication graph has a directed spanning tree. Finally, the convergence speeds of fractional‐order systems are compared, and it is discovered that the convergence of systems is faster using the control law based on error predictor than using the common one.

Distributed Fixed‐Time Coordinated Tracking for Nonlinear Multi‐Agent Systems Under Directed Graphs

“…where y ∈ R + ∪ {0}, , > 0, > 1. Then, the equilibrium is fixed-time stable for (7) and the following upper bound of the settling time T holds…”

“…According to the number of leaders in the network, existing explorations about the consensus problem are classified into three subareas, i.e., leaderless consensus without leaders, consensus tracking with a single leader, and containment control with multiple leaders. For leaderless consensus, control strategies are proposed for first-order [5], second-order [6], fractional-order [7], linear [8,9] multi-agent systems, and for synchronization [10]. For consensus tracking, the aim is to drive the states of followers to reach the state of the leader.…”

Consensus of fractional‐order multi‐agent systems using iterative learning control in the sense of Lebesgue‐p norm

“…Cao et al [22,23] first studied the consensus problem of fractional‐order multi‐agents and provided the uniform convergence conditions for FOMASs. Bai et al [24] studied the consensus problem of FOMASs in fixed reference state and time‐varying reference state respectively. For nonlinear fractional multi‐agents with leaders, Yu et al [25] designed the control quantity of each agent to achieve uniform convergence according to the graph theory and the Lyapunov method.…”

Consensus of Delayed Fractional‐Order Multiagent Systems Based on State‐Derivative Feedback

“…In [11,12], the proportional-integral differential (PID) controllers whose dynamics were fractionalorder dynamics were proposed and the performance of the fractional-order PID controllers was superior to that of the classical integer-order ones. Moreover, it has been stated in [13] that fractional derivatives were excellent tools for representing the memories and hereditary effects of all manner of materials and processes.…”

“…Since then, many research results have been continuously springing up about consensus problems of FMSs [13][14][15][16][17]. The consensus problem of FMSs with a reference state was studied in [13,14]. The consensus of FMSs about event-triggered control was investigated in [15].…”