Leader-following consensus of linear multi-agent systems with randomly occurring nonlinearities and uncertainties and stochastic disturbances

Fixed-time sliding-mode distributed consensus and formation control of disturbed fractional-order multi-agent systems

In this paper, fixed-time consensus and formation control for fractional-order multi-agent systems with a dynamic virtual leader in the presence of external disturbances is investigated. Consensus is achieved in fixed-time, i.e., with a finite settling time whose upper bound is independent of the initial conditions of the agents' states. A new distributed sliding-mode control with neighborhood-based error variable is proposed to track a virtual leader in order to achieve a desired consensus in the presence of disturbances. Furthermore, the fractional Lyapunov stability theorem has been employed to prove the fixed-time stability and to estimate the upper bound of convergence. The formation of agents has also been investigated for the agents of fractional-order. Finally, several numerical simulations are provided to determine the effectiveness of the design method.

Quasi-Consensus of Disturbed Nonlinear Multiagent Systems with Event-Triggered Impulsive Control

Considering the external disturbances, in this paper, the quasi-consensus of multiagent systems is studied via event-triggered impulsive control. By designing a novel event-triggered mechanism (ETM), sufficient conditions to realize leader-following quasi-consensus are derived with event-triggered impulsive control. Additionally, Zeno behavior is also excluded. It is shown that the event-triggered frequency is closely related to the parameters selected in the designed ETM, and less conservative results can be obtained compared with the existing results. Finally, a simulation example is given to demonstrate the effectiveness of our proposed results.

Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons

An algorithm for synchronization of a network composed of interconnected Hindmarsh–Rose neurons is presented. Delays are present in the interconnections of the neurons. Noise is added to the controlled input of the neurons. The synchronization algorithm is designed using convex optimization and is formulated by means of linear matrix inequalities via the stochastic version of the Razumikhin functional. The recovery and the adaptation variables are also synchronized; this is demonstrated with the help of the minimum-phase property of the Hindmarsh–Rose neuron. The results are illustrated by an example.

Observer-Based Consensus of Higher-Order Nonlinear Heterogeneous Multiagent Systems with Unmatched Uncertainties: Application on Robotic Systems

The consensus of higher-order nonlinear heterogeneous multiagent systems with matched and unmatched uncertainties is studied in this paper. The distributed observer-based controllers for multiagent systems are achieved using a fixed-time sliding mode controller based on the disturbance observer. For this purpose, the disturbance observers are designed for finite-time estimation of matched and unmatched uncertainties. Using the estimated values, the fixed-time distributed sliding mode controllers are designed and the consensus protocol is achieved. In this regard, a theorem is proved, which guarantees the fixed-time convergence of consensus errors. The effectiveness of the proposed distributed controllers has been validated through simulations for two robotic multiagent systems and a numerical example.

Distributed Adaptive Neural Network Output Tracking of Leader-Following High-Order Stochastic Nonlinear Multiagent Systems With Unknown Dead-Zone Input

This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.