This article investigates the consensus problem for a class of fractional-order multi-agent systems with input delay. Each follower is modeled as a system with input delay and nonlinear dynamics. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, dynamic surface control technology is introduced into an adaptive neural network backstepping controller. A dynamic event-triggered scheme without Zeno behavior is considered, which can reduce the utilization of communication resources. The sliding mode control technology is introduced to enhance robustness. The Pade delay approximation method is extended to fractional-order systems, which converts the original systems into systems without input delay. The stability of systems is ensured by the constructed Lyapunov functions. Examples and simulation results show that the consensus tracking errors can quickly converge and all the followers can synchronize to the leader by the proposed method.

This paper investigates the fractional order chaotic systems synchronization with input delay. To reduce the utilization of communication resources and achieve system synchronization, an adaptive neural network backstepping sliding mode controller is proposed based on event-triggered scheme without Zeno behavior. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. The sliding term is introduced to enhance robustness. The Pade delay approximation method is used to handle the input delay, which can reduce the analysis complexity of fractional order chaotic systems with input delay. The unknown nonlinear functions and uncertain disturbances are approximated by the RBF neural network. An observer is used for state estimation of the fractional order system. By applying the Lyapunov stability theory, we can prove that the all closed-loop signals are bounded. Examples and simulations prove the feasibility of the proposed control method.

This paper studies the containment control problem for a class of fractional order nonlinear multiagent systems in the presence of arbitrary switchings, unmeasured states, and quantized input signals by a hysteresis quantizer. Under the framework of the Lyapunov function theory, this paper proposes an event-triggered adaptive neural network dynamic surface quantized controller, in which dynamic surface control technology can avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously. Radial basis function neural networks (RBFNNs) are used to approximate the unknown nonlinear functions, and an observer is designed to obtain the unmeasured states. The proposed distributed protocol can ensure all the signals remain semi-global uniformly ultimately bounded in the closed-loop system, and all followers can converge to the convex hull spanned by the leaders’ trajectory. Utilizing the combination of an event-triggered scheme and quantized control technology, the controller is updated aperiodically only at the event-sampled instants such that transmitting and computational costs are greatly reduced. Simulations compare the event-triggered scheme without quantization control technology with the control method proposed in this paper, and the results show that the event-triggered scheme combined with the quantization mechanism reduces the number of control inputs by 7% to 20%.