Self-Triggered Leader-Following Consensus for High-Order Nonlinear Multiagent Systems via Dynamic Output Feedback Control

Distributed Estimator-Based Event-Triggered Neuro-Adaptive Control for Leader-Follower Consensus of Strict-Feedback Nonlinear Multiagent Systems

This article investigates the leader-follower consensus problem for strict-feedback nonlinear multiagent systems under a dual-terminal event-triggered mechanism. Compared with the existing event-triggered recursive consensus control design, the primary contribution of this article is the development of a distributed estimator-based event-triggered neuro-adaptive consensus control methodology. In particular, by introducing a dynamic event-triggered communication mechanism without continuous monitoring neighbors' information, a novel distributed event-triggered estimator in chain form is constructed to provide the leader's information to the followers. Subsequently, the distributed estimator is utilized to consensus control via backstepping design. To further decrease information transmission, a neuro-adaptive control and an event-triggered mechanism setting on the control channel are codesigned via the function approximate approach. A theoretical analysis shows that all the closed-loop signals are bounded under the developed control methodology, and the estimation of the tracking error asymptotically converges to zero, i.e., the leader-follower consensus is guaranteed. Finally, simulation studies and comparisons are conducted to verify the effectiveness of the proposed control method.

Output Feedback-Based Consensus for Nonlinear Multiagent Systems: The Event-Triggered Communication Strategy

The current investigation explores the leader-following consensus problem for nonlinear multiagent systems under the output feedback control mechanism and the event-triggered communication mechanism. Owing to the physical instrument constraints, a significant portion of the state variables is not readily available. Therefore, this article put forward a distributed event-based leader-following consensus protocol only using agents' relative output measurements and underlying neighbors. Furthermore, this article develops two event-triggered mechanisms simultaneously, one is the event-triggered communication mechanism in the sensor-to-controller channel, and another is the event-triggered controller update in the controller-to-actuator track. Besides that, it is proven that the developed event-triggered control protocol can settle the leader-following consensus problem of the nonlinear multiagent systems, and the Zeno behavior is excluded in both the channels. Finally, we perform two simulation examples to illustrate the efficacy of the obtained results.

Event-Triggered Bounded Consensus Tracking for Second-Order Nonlinear Multi-Agent Systems with Uncertainties

This paper is concerned with event-triggered bounded consensus tracking for a class of second-order nonlinear multi-agent systems with uncertainties (MASs). Remarkably, the considered MASs allow multiple uncertainties, including unknown control coefficients, parameterized unknown nonlinearities, uncertain external disturbances, and the leader's control input being unknown. In this context, a new estimate-based adaptive control protocol with a triggering mechanism is proposed. We rule out Zeno behavior by testifying that the lower bound on the interval between two consecutive events is positive. It is shown that under the designed protocol, all signals caused by the closed-loop systems are bounded globally uniformly and tracking errors ultimately converge to a bounded set. The effectiveness of the devised control protocol is demonstrated through a simulation example.

Distributed UAV Swarm Formation and Collision Avoidance Strategies Over Fixed and Switching Topologies

This article proposes a controlling framework for multiple unmanned aerial vehicles (UAVs) to integrate the modes of formation flight and swarm deployment over fixed and switching topologies. Formation strategies enable UAVs to enjoy key collective benefits including reduced energy consumption, but the shape of the formation and each UAV's freedom are significantly restrained. Swarm strategies are thus proposed to maximize each UAV's freedom following simple yet powerful rules. This article investigates the integration and switch between these two strategies, considering the deployment environment factors, such as poor network conditions and unknown and often highly mobile obstacles. We design a distributed formation controller to guide multiple UAVs in orderless states to swiftly reach an intended formation. Inspired by starling birds and similar biological creatures, a distributed collision avoidance controller is proposed to avoid unknown and mobile obstacles. We further illustrated the stability of the controllers over both fixed and switching topologies. The experimental results confirm the effectiveness of the framework.

Consensus for Second-Order Multiagent Systems Under Two Types of Sampling Mechanisms: A Time-Varying Gain Observer Method

This article considers the consensus of second-order multiagent systems (MASs) under a directed communication topology. By introducing time-varying gains into observers, two types of novel continuous-discrete-time observers are presented to estimate state information of agents under two sampling mechanisms, respectively, namely: 1) a synchronous nonuniform sampling (SNS) mechanism and 2) an asynchronous nonuniform sampling (ANS) mechanism. A new design method of the time-varying gain observer is proposed, in that it can allow for one to select a consensus protocol with lower cost observers to attain the consensus task. Only sampled position information needs to be transmitted in designing consensus protocols for the MSAs, and neither velocity information nor control input information is required. Under the SNS mechanism, a consensus condition is obtained and it is shown that the introduction of time-varying gains in the observers indeed can improve their convergence. Under the ANS mechanism, the corresponding consensus protocol allows the sampling and transmission of different agents to be asynchronous and aperiodic, which means that each agent may sample and transmit its information in line with its own sampling requirements. Furthermore, each sampling period can be arbitrarily selected within a certain range while ensuring the consensus of the MASs. Finally, numerical examples are given to illustrate the effectiveness of the obtained results.

A Dynamic Gain Approach to Consensus Control of Nonlinear Multiagent Systems With Time Delays

This article proposes a dynamic gain approach for investigating the leader-follower consensus problem of nonlinear multiagent systems with both distributed delays and discrete delays. It is assumed that each agent is in the strict-feedback form and satisfies the Lipschitz condition with an unknown constant. A novel dynamic gain observer is first constructed for each follower by only utilizing the output information of the follower and its neighbors. By introducing an observer, a distributed output-feedback control protocol is designed for each follower agent under a directed communication topology. It is proved by the Lyapunov-Razumikhin theorem that the consensus of the multiagent system is achieved with the proposed consensus protocol. Different from the existing results, the dynamic gain is constructed for each follower to propose the consensus protocol, without resorting to the celebrated backstepping technique. Moreover, the time-varying gain is designed in a uniform framework. The effectiveness of the proposed approaches is illustrated by a simulation example.

On Iterative Proportional Updating: Limitations and Improvements for General Population Synthesis

Population synthesis is the foundation of the agent-based social simulation. Current approaches mostly consider basic population and households, rather than other social organizations. This article starts with a theoretical analysis of the iterative proportional updating (IPU) algorithm, a representative method in this field, and then gives an extension to consider more social organization types. The IPU method, for the first time, proves to be unable to converge to an optimal population distribution that simultaneously satisfies the constraints from individual and household levels. It is further improved to a bilevel optimization, which can solve such a problem and include more than one type of social organization. Numerical simulations, as well as population synthesis using actual Chinese nationwide census data, support our theoretical conclusions and indicate that our proposed bilevel optimization can both synthesize more social organization types and get more accurate results.

Leader-Following Mean-Square Consensus of Stochastic Multiagent Systems With ROUs and RONs via Distributed Event-Triggered Impulsive Control

Based on the distributed event-triggered impulsive mechanism, the leader-following mean-square consensus of stochastic multiagent systems with randomly occurring uncertainties and randomly occurring nonlinearities is investigated for the first time in this article. In order to make better use of the limited communication resources, we proposed some novel communication rules among agents and corresponding control protocol. Moreover, some new triggering functions are designed for different types of agents, which cannot only ensure that the Zeno behavior can be excluded but also make the upper bound of impulsive interval in the total time sequence satisfy a newly proposed constraint condition. When the expected value of the triggering function of the i th agent is non-negative within an event time interval, the impulsive control will be triggered. If the system achieves the consensus, the triggering events of all agents will not occur after some time. The original system is transformed into the delay system by using the input delay approach. Based on the Lyapunov stability theory, several sufficient delay-independent criteria for mean-square consensus are derived by a class of Halanay impulsive differential inequalities. Finally, the effectiveness of theoretical results is illustrated by numerical simulation examples.

Event-Triggered/Self-Triggered Leader-Following Control of Stochastic Nonlinear Multiagent Systems Using High-Gain Method

In this article, the event-triggered and self-triggered leader-following output-feedback control problems are investigated for a class of high-order stochastic nonlinear multiagent systems (MASs) under an undirected graph. First, using the high-gain method, the observer is designed to estimate the unmeasured state variables of the given nonlinear system. Then, by introducing an internal dynamic variable, a distributed Zeno-free dynamic event-triggered controller is constructed. Compared with the static event-triggering results, the interevent time of the proposed dynamic event-triggering mechanism is shown to be prolonged and, thus, the advantages of the event-triggered control approaches can be enhanced. Further, to avoid continuously monitoring the states, a Zeno-free self-triggering mechanism is given. It is shown that the expectations of the output tracking errors converge to an arbitrarily small set if the diffusion terms are different for all agents, and that the expectations of all state tracking errors converge to an arbitrarily small set if the diffusion terms are the same for all agents. Finally, simulation studies are given to illustrate the effectiveness of the proposed methods.

Distributed Containment Control for Nonlinear Stochastic Multiagent Systems

This paper addresses the output feedback distributed containment control problem for a class of nonlinear stochastic multiagent systems under a fixed directed graph. Existing works usually design the containment control protocol using backstepping design method based on a conservative Lipschitz condition on nonlinear functions, which has a tedious control design procedure. In this paper, a new output feedback distributed containment control algorithm is proposed based on a novel dynamic compensator, which can not only simplify the control design procedure but also relax the condition on nonlinear terms. The proposed distributed containment protocol for each agent depends only on the agent output and the relative outputs of its neighbor agents, and can reduce the communication burden between the agents. Based on the Lyapunov stability theory, it is proved that the outputs of the followers are driven into the convex hull spanned by the outputs of the leaders with the proposed linear controller. Finally, the effectiveness of the theoretical results is illustrated by simulation examples.

H∞ synchronization of delayed neural networks via event-triggered dynamic output control

This paper investigates H_∞ exponential synchronization (ES) of neural networks (NNs) with delay by designing an event-triggered dynamic output feedback controller (ETDOFC). The ETDOFC is flexible in practice since it is applicable to both full order and reduced order dynamic output techniques. Moreover, the event generator reduces the computational burden for the zero-order-hold (ZOH) operator and does not induce sampling delay as many existing event generators do. To obtain less conservative results, the delay-partitioning method is utilized in the Lyapunov-Krasovskii functional (LKF). Synchronization criteria formulated by linear matrix inequalities (LMIs) are established. A simple algorithm is provided to design the control gains of the ETDOFC, which overcomes the difficulty induced by different dimensions of the system parameters. One numerical example is provided to demonstrate the merits of the theoretical analysis.

Neural-Network-Based Adaptive Event-Triggered Consensus Control of Nonstrict-Feedback Nonlinear Systems

The event-triggered consensus control problem is studied for nonstrict-feedback nonlinear systems with a dynamic leader. Neural networks (NNs) are utilized to approximate the unknown dynamics of each follower and its neighbors. A novel adaptive event-trigger condition is constructed, which depends on the relative output measurement, the NN weights estimations, and the states of each follower. Based on the designed event-trigger condition, an adaptive NN controller is developed by using the backstepping control design technique. In the control design process, the algebraic loop problem is overcome by utilizing the property of NN basis functions and by designing novel adaptive parameter laws of the NN weights. The proposed adaptive NN event-triggered controller does not need continuous communication among neighboring agents, and it can substantially reduce the data communication and the frequency of the controller updates. It is proven that ultimately bounded leader-following consensus is achieved without exhibiting the Zeno behavior. The effectiveness of the theoretical results is verified through simulation studies.

Observer-Based Event-Triggered Adaptive Fuzzy Control for Leader-Following Consensus of Nonlinear Strict-Feedback Systems

In this article, the leader-following consensus problem via the event-triggered control technique is studied for the nonlinear strict-feedback systems with unmeasurable states. The follower's nonlinear dynamics is approximated using the fuzzy-logic systems, and the fuzzy weights are updated in a nonperiodic manner. By introducing a fuzzy state observer to reconstruct the system states, an observer-based event-triggered adaptive fuzzy control and a novel event-triggered condition are designed, simultaneously. In addition, the nonzero positive lower bound on interevent intervals is presented to avoid the Zeno behavior. It is proved via an extension of the Lyapunov approach that ultimately bounded control is achieved for the leader-following consensus of the considered multiagent systems. One remarkable advantage of the proposed control protocol is that the control law and fuzzy weights are updated only when the event-triggered condition is violated, which can greatly decrease the data transmission and communication resource. The simulation results are provided to show the effectiveness of the proposed control strategy and the theoretical analysis.

Fuzzy Adaptive Two-Bit-Triggered Control for a Class of Uncertain Nonlinear Systems With Actuator Failures and Dead-Zone Constraint

This article investigates a fuzzy adaptive two-bit-triggered control for uncertain nonlinear systems with actuator failures and dead-zone constraint. Actuator failures and dead-zone constraint exist frequently in practical systems, which will affect the system performance greatly. Based on the improved fuzzy-logic systems (FLSs), a fuzzy adaptive compensation control is established to address these issues. The approximation error is introduced to the control design as a time-varying function. In addition, for the limited transmission resources of the practical system, a two-bit-triggered control mechanism is proposed to further save system transmission resources. It is proved that the proposed method can guarantee the system tracking performance and all the signals are bounded. Its effectiveness is verified by the simulation examples.

Observer-Based Event-Triggered Predictive Control for Networked Control Systems under DoS Attacks

This paper studies the problem of DoS attack defense based on static observer-based event-triggered predictive control in networked control systems (NCSs). First, under the conditions of limited network bandwidth resources and the incomplete observability of the state of the system, we introduce the event-triggered function to provide a discrete event-triggered transmission scheme for the observer. Then, we analyze denial-of-service (DoS) attacks that occur on the network transmission channel. Using the above-mentioned event-triggered scheme, a novel class of predictive control algorithms is designed on the control node to proactively save network bandwidth and compensate for DoS attacks, which ensures the stability of NCSs. Meanwhile, a closed-loop system with an observer-based event-triggered predictive control scheme for analysis is created. Through linear matrix inequality (LMI) and the Lyapunov function method, the design of the controller, observer and event-triggered matrices is established, and the stability of the scheme is analyzed. The results show that the proposed solution can effectively compensate DoS attacks and save network bandwidth resources by combining event-triggered mechanisms. Finally, a smart grid simulation example is employed to verify the feasibility and effectiveness of the scheme's defense against DoS attacks.

Distributed Adaptive Fuzzy Event-Triggered Containment Control of Nonlinear Strict-Feedback Systems

In this paper, the adaptive fuzzy event-triggered containment control problem is addressed for uncertain nonlinear strict-feedback systems guided by multiple leaders. A novel distributed adaptive fuzzy event-triggered containment control is designed only using the information of the individual follower and its neighbors. Moreover, a distributed event-trigger condition with an adjustable threshold is developed simultaneously. The designed containment control law is updated in an aperiodic manner, only when event-triggered errors exceed tolerable thresholds. It is proved that the uniformly ultimately bounded containment control can be achieved, and there is no Zeno behavior exhibited by applying the proposed control scheme. Simulation studies are outlined to illustrate the effectiveness of the theoretical results and the advantages of the event-triggered containment control proposed in this paper.

Command Filter-Based Adaptive NN Control for MIMO Nonlinear Systems With Full-State Constraints and Actuator Hysteresis

This article studies the issue of adaptive neural network (NN) control for strict-feedback multi-input and multioutput (MIMO) nonlinear systems with full-state constraints and actuator hysteresis. Radial basis function NNs (RBFNNs) are introduced to approximate unknown nonlinear functions. The command filter is adopted to solve the issue of "explosion of complexity." By applying a one-to-one nonlinear mapping, the strict-feedback system with full-state constraints is converted into a new pure-feedback system without state constraints, and a novel NN control method is proposed. The stability of the closed-loop system is proved via the Lyapunov stability theory, and the tracking errors converge to small residual sets. The simulation results are given to confirm the validity of the proposed method.

Observer-Based Event-Triggered Control for Networked Linear Systems Subject to Denial-of-Service Attacks

This paper is concerned with the observer-based event-triggered control for a continuous networked linear system subject to denial-of-service (DoS) attacks, where the attacks are launched periodically to block the data transmission in control channels. First, a new observer state-based resilient event-triggering scheme is developed in the presence of DoS attacks. Second, a novel event-based switched system model is established by considering the effect of the event-triggering scheme and DoS attacks simultaneously. By virtue of this new model combined with a piecewise Lyapunov-Krasovskii functional method, the sufficient conditions are derived to guarantee exponential stability of the resulting switched system. It is shown that the proposed results can establish a quantitative relationship among the launching/sleeping periods of the attacks, the event-triggering parameters, the sampling period, and the exponential decay rate. Third, criteria for designing a desired observer-based event-triggered controller are provided and expressed in terms of a set of linear matrix inequalities. Finally, an offshore structure model is presented to illustrate the efficiency of the developed control method.

Consensus Tracking Control of Switched Stochastic Nonlinear Multiagent Systems via Event-Triggered Strategy

In this paper, the consensus tracking problem is investigated for a class of continuous switched stochastic nonlinear multiagent systems with an event-triggered control strategy. For continuous stochastic multiagent systems via event-triggered protocols, it is rather difficult to avoid the Zeno behavior by the existing methods. Thus, we propose a new protocol design framework for the underlying systems. It is proven that follower agents can almost surely track the given leader signal with bounded errors and no agent exhibits the Zeno behavior by the given control scheme. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the new design techniques.

Cooperative Control of Multiple Nonlinear Benchmark Systems Perturbed by Second-Order Moment Processes

This paper studies the cooperative control problem of multiple nonlinear benchmark systems perturbed by second-order moment processes. The nonlinear benchmark system consists of a moving car and a rolling ball in oscillating surroundings. When the leader is only accessible to a small part of the followers in a directed graph, a new vectorial backstepping method is proposed for the design of distributed cooperative control laws. By using stochastic analysis techniques and algebra graph theory, it is shown that the cooperative control problem under consideration is solvable. Specifically, the errors between the followers' outputs and the leader's output can be made arbitrarily small while keeping all states of the closed-loop system bounded in probability. Finally, the effectiveness of the proposed control scheme is demonstrated through a simulation example.