Synchronization and Consensus in Networks of Linear Fractional-Order Multi-Agent Systems via Sampled-Data Control

Event-Triggered Adaptive Neural Network Tracking Control for Uncertain Systems With Unknown Input Saturation Based on Command Filters

This brief presents a modified event-triggered command filter backstepping tracking control scheme for a class of uncertain nonlinear systems with unknown input saturation based on the adaptive neural network (NN) technique. First, the virtual control functions are reconstructed to address the uncertainties in subsystems by using command filters. A piecewise continuous function is employed to deal with the unknown input saturation problem. Next, an event-triggered tracking controller is developed by utilizing the adaptive NN technique. Compared with standard NN control schemes based on multiple-function-approximators, our controller only requires a single NN. The closed-loop system stability is analyzed based on the Lyapunov stability theorem, and it is shown that the Zeno behavior is also avoided under the designed event-triggering mechanism. Simulation studies are performed to validate the effectiveness of our controller.

Quasi-synchronization for variable-order fractional complex dynamical networks with hybrid delay-dependent impulses

This paper focuses on addressing the problem of quasi-synchronization in heterogeneous variable-order fractional complex dynamical networks (VFCDNs) with hybrid delay-dependent impulses. Firstly, a mathematics model of VFCDNs with short memory is established under multi-weighted networks and mismatched parameters, which is more diverse and practical. Secondly, under the framework of variable-order fractional derivative, a novel fractional differential inequality has been proposed to handle the issue of quasi-synchronization with hybrid delay-dependent impulses. Additionally, the quasi-synchronization criterion for VFCDNs is developed using differential inclusion theory and Lyapunov method. Finally, the practicality and feasibility of this theoretical analysis are demonstrated through numerical examples.

Positive Consensus of Fractional-Order Multiagent Systems Over Directed Graphs

This article investigates the positive consensus problem of a special kind of interconnected positive systems over directed graphs. They are composed of multiple fractional-order continuous-time positive linear systems. Unlike most existing works in the literature, we study this problem for the first time, in which the communication topology of agents is described by a directed graph containing a spanning tree. This is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains, which renders the positivity analysis fairly challenging. Based on the existing results in spectral graph theory, fractional-order systems (FOSs) theory, and positive systems theory, we derive several necessary and/or sufficient conditions on the positive consensus of fractional-order multiagent systems (PCFMAS). It is shown that the protocol, which is designed for a specific graph, can solve the positive consensus problem of agents over an additional set of directed graphs. Finally, a comprehensive comparison study of different approaches is carried out, which shows that the proposed approaches have advantages over the existing ones.

Reset Event-Triggered Adaptive Fuzzy Consensus for Nonlinear Fractional-Order Multiagent Systems With Actuator Faults

This article studies the problem of event-triggered adaptive fault-tolerant fuzzy output feedback consensus tracking control for nonlinear fractional-order multiagent systems with actuator failures under a directed graph. Considering the fact that the actual system works near the equilibrium point most of the time, a novel dynamic event-triggering strategy with the reset mechanism is proposed, where the dynamic threshold can be actively adjusted according to the preset conditions, so that the resource utilization can be further reduced. Based on an improved event-based consensus error, the state estimator about the derivative of reference trajectory and the adaptive law about the information of graph are constructed, which makes distributed consensus tracking control achieved without obtaining global information. Then, by introducing two adaptive compensating terms to deal with actuator failures and event-triggered measurement errors, it is shown in the sense of fractional-order stability criterion that tracking errors can converge to a compact set even if the fault parameters and modes are completely unknown. Finally, the correctness of the presented method is verified by a simulation example.

Leader-Follower Asymptotic Consensus Control of Multiagent Systems: An Observer-Based Disturbance Reconstruction Approach

In this article, a leader-follower asymptotic consensus control strategy is developed for a class of linear multiagent systems (MASs) with unknown external disturbances and measurement noises. First, the preconditions, the minimum phase condition (MPC) and observer matching condition (OMC), are discussed in detail, and an equivalent result under these two preconditions is given. In this way, the corresponding results from Corless and Tu (1998) are improved. Meanwhile, a reduced-order observer is designed for a constructed augmented system to estimate the system states and noises of each agent. Next, with the help of a traditional interval observer, a novel unknown disturbance reconstruction method is developed, and the reconstruction can converge to the unknown disturbance asymptotically and decouple from the control input. The subsequent asymptotic consensus is accomplished by utilizing an observer-based control scheme, with its design satisfying the so-called separation principle. Finally, two simulation examples are given to verify the effectiveness and show the advantages of the proposed methods.

Distributed Model-Free Sliding-Mode Predictive Control of Discrete-Time Second-Order Nonlinear Multiagent Systems With Delays

In this article, the tracking problem of networked discrete-time second-order nonlinear multiagent systems (MASs) is studied. First, for the MASs without communication delay, a novel method, called distributed model-free sliding-mode control algorithm is proposed, which can make the system converge quickly without the accurate model. Furthermore, for the MASs with delay, in order to eliminate the influence of time delay on the system, a distributed model-free sliding-mode predictive control strategy based on time-delay compensation technology is proposed, which can actively compensate for time delay while ensuring system stability and consensus tracking performance requirements. Both the simulation and experiment results reveal the superiority of the proposed methods.

Distributed Bipartite Adaptive Event-Triggered Fault-Tolerant Consensus Tracking for Linear Multiagent Systems Under Actuator Faults

This article considers the distributed bipartite adaptive event-triggered fault-tolerant consensus tracking issue for linear multiagent systems in the presence of actuator faults based on the output feedback control protocol. Both time-varying additive and multiplicative actuator faults are taken into account in the meantime. And the upper/lower bounds of actuator faults are not required to be known. First, the state observer is designed to settle the occurrence of unmeasurable system states. Two kinds of event-triggered mechanisms are then developed to schedule the interagent communication and controller updates. Next, with the developed event-triggered mechanisms, a novel observer-based bipartite adaptive control strategy is proposed such that the fault-tolerant control problem can be addressed. Compared with some related works on this topic, our control scheme can achieve the intermittent communication and intermittent controller updates, and the more general actuator faults and network topology are considered. It is proved that the exclusion of Zeno behavior can be realized. Finally, three illustrative examples are given to demonstrate the feasibility of the main theoretical findings.

Large-Scale Multiagent System Tracking Control Using Mean Field Games

This article studies the tracking control problem with a large-scale group of agents. Unlike traditional control techniques used in multiagent systems (MASs), a new type of intelligent design is needed to handle the intractable "Curse of Dimensionality" caused by the extremely large number of agents. To address this challenge, the mean field game (MFG) theory has been embedded into reinforcement learning to advance intelligent tracking control with large-scale MAS. Specifically, MFG-based control can calculate the optimal strategy based on one unified fix-dimension probability density function (pdf) instead of high-dimensional large-scale MAS information collected from individual agents. Moreover, the approximate dynamic programming technique is adopted to generate a new type of MFG-based algorithm. Each agent has three neural networks (NNs) to approximate the solution of the mean field type control. In addition to the algorithm development, the performance of the NNs is also analyzed using the Lyapunov method. Finally, the linear and nonlinear tracking control simulations are given to evaluate the algorithm's performance.

Uniform Stability of Complex-Valued Neural Networks of Fractional Order With Linear Impulses and Fixed Time Delays

As a generation of the real-valued neural network (RVNN), complex-valued neural network (CVNN) is based on the complex-valued (CV) parameters and variables. The fractional-order (FO) CVNN with linear impulses and fixed time delays is discussed. By using the sign function, the Banach fixed point theorem, and two classes of activation functions, some criteria of uniform stability for the solution and existence and uniqueness for equilibrium solution are derived. Finally, three experimental simulations are presented to illustrate the correctness and effectiveness of the obtained results.

Distributed Observer-Based Leader-Follower Consensus of Multiple Euler-Lagrange Systems

This article investigates the leader-follower consensus problem of multiple Euler-Lagrange (EL) systems, where each agent suffers uncertain external disturbances, and the communication links among agents experience faults. Besides, we consider a more general case that only a portion of followers can measure partial components of leader's output and access the dynamic information of leader. The main idea of solving the consensus problem in this article is proceeded in two steps. First, we design an adaptive distributed observer to estimate the full state information of leader in real time with resilience to communication link faults. Second, based on the proposed distributed observer, we propose a proportional-integral (PI) control protocol for each agent to track the trajectory of leader, which is model-independent and robust to uncertain external disturbances. Distinct from the existing leader-follower consensus protocols of multiple EL systems, the proposed distributed observer-based PI consensus protocol in this article is model-independent, which is irrelevant to the structures or features of EL system model. Finally, we present a simulation example to show the resilience of the above adaptive distributed observer and the robustness of the distributed observer-based consensus protocol.

Decentralized Adaptive Optimal Tracking Control for Massive Autonomous Vehicle Systems With Heterogeneous Dynamics: A Stackelberg Game

In this article, a decentralized optimal tracking control problem has been studied for a large-scale autonomous vehicle system with heterogeneous system dynamics. Due to the ultralarge number of agents, the notorious "curse of dimension" problem as well as the unrealistic assumption of the existence of reliable very large-scale communication links in uncertain environments have challenged the traditional multiagent system (MAS) algorithms for decades. The emerging mean-field game (MFG) theory has recently been widely adopted to generate a decentralized control method that deals with those challenges by encoding the large scale MASs' information into a novel time-varying probability density functions (PDF) which can be obtained locally. However, the traditional MFG methods assume all agents are homogeneous, which is unrealistic in practical industrial applications, e.g., Internet of Things (IoTs), and so on. Therefore, a novel mean-field Stackelberg game (MFSG) is formulated based on the Stackelberg game, where all the agents have been classified as two different categories where one major leader's decision dominates the other minor agents. Moreover, a hierarchical structure that treats all minor agents as a mean-field group is developed to tackle the assumption of homogeneous agents. Then, the actor-actor-critic-critic-mass ( A²C²M ) algorithm with five neural networks is designed to learn the optimal policies by solving the MFSG. The Lyapunov theory is utilized to prove the convergence of A²C²M neural networks and the closed-loop system's stability. Finally, a series of numerical simulations are conducted to demonstrate the effectiveness of the developed method.