Neural Network-Based Fixed-Time Tracking and Containment Control of Second-Order Heterogeneous Nonlinear Multiagent Systems.

This study concentrates on the fixed-time tracking consensus and containment control of second-order heterogeneous nonlinear multiagent systems (MASs) with and without measurable velocity under directed topology. By defining a time-varying scaling function and approximating the unknown nonlinear dynamics with radial basis function neural networks (RBFNNs), a novel distributed protocol for solving the fixed-time tracking consensus and containment control problems of second-order heterogeneous nonlinear MASs with full states available is proposed based on a nonsingular sliding-mode control method constructed by designing a prescribed-time convergent sliding surface. For the scenario of immeasurable velocity, a fixed-time convergent states' observer is designed to reveal the velocity information when the unknown linearity is bounded. Subsequently, a distributed fixed-time consensus protocol based on observed velocity information is proposed for the extended results. Ultimately, the acquired results are verified by three simulation examples.

Neuroadaptive Impulsive Control on Consensus of Uncertain Multiagent Systems Using Continuous and Sampled Information.

This article considers the consensus problem of uncertain multiagent systems, which is addressed by neuroadaptive impulsive control schemes. The proposed control schemes indicate that the communication among agents only occurs impulsively, while the dynamics uncertainty is addressed by adaptive schemes using neural networks. Based on such approaches, two specific control schemes are designed. One is that with impulsive feedback, the control scheme uses continuous-time information, which implies that the adaptive process is continuous over time. Another is that by adopting sampled information, the update of all systems, including the feedbacks on agents, the update of neural networks, and the estimation for uncertainty, can be executed only at impulsive instants. The latter case can reduce the energy cost for communication and control, but extra assistant systems are required. The estimation and consensus prove to be achieved with errors if some conditions are fulfilled. Numerical simulations, including a practical system example, are presented.

Impulsive Communication With Full and Partial Information for Adaptive Tracking Consensus of Uncertain Second-Order Multiagent Systems.

The uncertainty of dynamics is often unavoidable in practical applications especially for networked control systems while energy cost reduction is a perpetual issue for engineering. With this motivation, this article considers the adaptive tracking consensus problem of uncertain second-order multiagent systems via impulsive communication. The tracking consensus is achieved by designing proper adaptive control schemes with neural networks. Two control strategies are proposed for different cases. One considers that all state information is available while another considers only partial information can be used. Estimators equipped by followers are designed, which do not need any information about neighbors during the time interval without communication. Even though the estimators and followers are under control continuously over time, the communication among all agents is only permitted at impulsive instants. In such situations, some sufficient conditions to guarantee the estimation and convergence are obtained for both cases. It is proved that by the proposed adaptive schemes for uncertain multiagent systems, errors exist both for estimation and consensus due to uncertain dynamics and adaptive schemes. Numerical simulations, including a practical example, are presented to illustrate the effectiveness of the proposed method.

Asynchronous Impulsive Protocols With Asymmetric Feedback Saturation on Leader-Based Formation Control of Multiagent Systems.

Saturation phenomena often exist due to limited system resources, and impulsive protocols can lead to a reduction in communication cost. From these issues, this article investigates a leader-based formation control problem of multiagent systems via asynchronous impulsive protocols with saturated feedback. General linear system models with and without finite time-varying time delays under asymmetric saturated feedback control are concurrently considered. The asynchronous impulsive protocols only permit communication at impulsive instants and each agent has its own communication instants independently. Moreover, to improve system performance, an offset only containing desired formation information is introduced. Finally, because the feedbacks are saturated, admissible regions are proved to exist, which are also estimated by a mean of optimization. Numerical simulations are presented to demonstrate the validity of the proposed schemes.

Impulsive Consensus of Multiagent Systems With Limited Bandwidth Based on Encoding-Decoding.

Energy constrains are always significant to be considered in control of multiagent systems. Besides, nonlinear phenomena are often involved into such systems. In this paper, we discuss the impulsive consensus problem of nonlinear multiagent systems via impulsive protocol with limited bandwidth communication based on encoding-decoding. The scheme based on encoding-decoding with impulsive protocol is introduced to multiagent systems in general directed networks topology of which the graph is strongly connected. The impulsive protocols and limited bandwidth communication enhance the performance on energy saving and the involvement of nonlinear dynamics could suit more real-world cases. The design of encoders and decoders is presented, which is the key to achieve the goal that the information exchanged is subject to limited bandwidth communication. The conditions to guarantee the impulsive consensus and the conditions to avoid quantizer saturation are obtained. Moreover, the convergence rate of such multiagent systems are also characterized by the analysis of the exponential consensus. The numerical simulations are presented to support the theoretical results.

Impulsive Consensus of Nonlinear Multi-Agent Systems via Edge Event-Triggered Control.

In this paper, we mainly investigate two kinds of consensuses of multi-agent systems (MASs) with nonlinear dynamics based on impulsive control, event-triggered control, and sampled-data control. The two types of impulsive protocols are proposed for the case without and with leader agent. Edge event-triggered technique is presented, where for each communication link, occurrence of edge event can activate the mutual state sampling and controller update of the corresponding agents. The control approach combines the characteristics of impulsive control and edge event-triggered control and is defined as "impulsive edge event-triggered control." It has good performance in robustness against disturbance and reduces the communication cost. The results with the aid of the Lyapunov function approach and stability theory of impulsive control show that if some sufficient conditions are satisfied, the consensus of MASs can be guaranteed and the rate of convergence can be exponentially estimated. Additionally, Zeno-behavior can be eliminated by using impulsive edge event-triggered control, which reduces the burden of event detectors. Finally, two simulations are provided to illustrate the effectiveness and performance of our theoretical analysis.

Asynchronous event-based sampling data for impulsive protocol on consensus of non-linear multi-agent systems.

In this paper, we discuss the consensus problem of non-linear multi-agent systems where an impulsive protocol with event-based asynchronously sampled data is adopted. Systems that communicate by data asynchronously sampled in limited time intervals are constructed. By separating time instants at which the sampling and communication occur into different ones, resources for such activations that every agent must execute can be reallocated to reduce the system load at communication instants. Event-based schemes are introduced to manipulate the sampling behavior. Two cases that with and without leader in directed networks topologies are both investigated. Sufficient conditions for system parameters and the event-based sampling schemes are given to guarantee the consensus. Numerical simulations are presented to illustrate the effectiveness of our proposed method.

Exponential consensus of discrete-time non-linear multi-agent systems via relative state-dependent impulsive protocols.

In this paper, we discuss the exponential consensus problem of discrete-time multi-agent systems with non-linear dynamics via relative state-dependent impulsive protocols. Impulsive protocols of which the impulsive instants are dependent on the weighted relative states of any two agents are introduced for general discrete-time multi-agent systems. The analysis of such impulsive protocols is transformed into an investigation on reduced fixed-time impulsive protocols by constructing a map, which is achieved mainly by a derived B-equivalence method in discrete-time domain. Our main results indicate that the exponential consensus of the multi-agent systems via relative state-dependent impulsive protocols can be achieved if the reduced systems via fixed-time impulsive protocols can achieve exponential consensus, which need to satisfy suitable sufficient conditions. Numerical simulations are presented to support the theoretical results.