Abstract
This paper investigates the consensus problem for the distributed multiagent system (MAS), where the trajectory of each agent is displayed by curvature and torsion, and the communication behaviors among agents are influenced by time delay and corrupted by noises. According to the Frenet–Serret formulas, a class of consensus protocols is designed for all agents, and a closed-loop system is obtained. Based on the Lyapunov method, several consensus criteria are derived, where the consensus criteria are characterized by curvature functions and torsion functions. Finally, one example shows the reliability of the proposed methods.
Highlights
In recent decades, the consensus problem of the multiagent system (MAS) has attracted the increasing attention of a large number of scholars, and the results have been widely used for tracking [1,2,3,4,5], formation control [6], distributed optimization monitoring [7, 8], and other purposes [9, 10].e consensus of MAS requires that the state of each node tends to be a common value
Based on a system transformation, the problem of group-couple is converted to a L2 control issue, and sufficient conditions are obtained for MAS, where the topology obeys a Markovian switching with unknown transition probabilities [17]
By considering the directed link failures or recoveries, a fault-tolerant control strategy with Markovian switching topology is provided for a nonlinear MAS, and some sufficient conditions of stochastic consensus are obtained, where MAS is in the presence of communication noises and actuator faults [30]
Summary
The consensus problem of the multiagent system (MAS) has attracted the increasing attention of a large number of scholars, and the results have been widely used for tracking [1,2,3,4,5], formation control [6], distributed optimization monitoring [7, 8], and other purposes [9, 10]. Under a designed switching signal set, the group consensus problem of the second-order MAS is studied in [24], where the switching topology obeys the Markovian chain, and by utilizing a state transformation method, two consensus sufficient criteria are established. Based on a system transformation, the problem of group-couple is converted to a L2 control issue, and sufficient conditions are obtained for MAS, where the topology obeys a Markovian switching with unknown transition probabilities [17]. By considering the directed link failures or recoveries, a fault-tolerant control strategy with Markovian switching topology is provided for a nonlinear MAS, and some sufficient conditions of stochastic consensus are obtained, where MAS is in the presence of communication noises and actuator faults [30]. Z+ is the positive integer set, Rn is the n- dimensional Euclidean space, C3 is the 3-times continuously differentiable, In is the n times n unit matrix, and 0 is the zero vector
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