Distributed consensus tracking for multiple uncertain nonlinear strict-feedback systems under a directed graph

Event-Triggered Adaptive Preassigned Finite-Time Consensus Control for Multiagent Systems With Nonlinear Faults

This article investigates a novel neuro-adaptive barrier Lyapunov function (BLF)-based event-triggered preassigned finite-time consensus control with asymptotic tracking for the nonlinear multiagent systems. The proposed approach is designed to broaden the scope of application by considering the high-order nonstrict-feedback dynamics of each agent with dynamic uncertainties subject to external disturbances and nonaffine nonlinear faults. A neural network (NN) is employed to approximate the unknown nonlinear terms. By fusing the NNs and Butterworth low-pass filter technique, the issues arising from the nonaffine nonlinear fault are addressed. To save the communication resources, a novel dynamic event-triggered mechanism based on an enhanced switching threshold is suggested. Additionally, a novel concept called the preassigned finite-time performance function (PFTPF) is defined to improve the transient and steady-state performances as well as providing faster response. The key feature of the proposed adaptive BLF-based control based on the bound estimation method is the introduction of a smooth function with decreasing variable which not only ensures that all the signals remain bounded and the synchronization errors are restricted within the PFTPF but also guarantees that the tracking errors asymptotically converge to zero. Finally, an illustrative example is provided to verify the feasibility of the proposed control approach.

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.

Distributed Optimization of Graph Convolutional Network Using Subgraph Variance

In recent years, distributed graph convolutional networks (GCNs) training frameworks have achieved great success in learning the representation of graph-structured data with large sizes. However, existing distributed GCN training frameworks require enormous communication costs since a multitude of dependent graph data need to be transmitted from other processors. To address this issue, we propose a graph augmentation-based distributed GCN framework (GAD). In particular, GAD has two main components: GAD-Partition and GAD-Optimizer. We first propose an augmentation-based graph partition (GAD-Partition) that can divide the input graph into augmented subgraphs to reduce communication by selecting and storing as few significant vertices of other processors as possible. To further speed up distributed GCN training and improve the quality of the training result, we design a subgraph variance-based importance calculation formula and propose a novel weighted global consensus method, collectively referred to as GAD-Optimizer. This optimizer adaptively adjusts the importance of subgraphs to reduce the effect of extra variance introduced by GAD-Partition on distributed GCN training. Extensive experiments on four large-scale real-world datasets demonstrate that our framework significantly reduces the communication overhead ( ≈ 50% ), improves the convergence speed ( ≈ 2 × ) of distributed GCN training, and obtains a slight gain in accuracy ( ≈ 0.45% ) based on minimal redundancy compared to the state-of-the-art methods.

Distributed Adaptive Formation Tracking for a Class of Uncertain Nonlinear Multiagent Systems: Guaranteed Connectivity Under Moving Obstacles

This article explores a guaranteed network connectivity problem during moving obstacle avoidance within a distributed formation tracking framework for uncertain nonlinear multiagent systems with range constraints. We investigate this problem based on a new adaptive distributed design using nonlinear errors and auxiliary signals. Within the detection range, each agent regards other agents and static or dynamic objects as obstacles. The nonlinear error variables for formation tracking and collision avoidance are presented, and the auxiliary signals in formation tracking errors are introduced to maintain network connectivity under the avoidance mechanism. The adaptive formation controllers using command-filtered backstepping are constructed to ensure closed-loop stability with collision avoidance and preserved connectivity. Compared with the previous formation results, the resulting features are as follows: 1) the nonlinear error function for the avoidance mechanism is considered an error variable, and an adaptive tuning mechanism for estimating the dynamic obstacle velocity is derived in a Lyapunov-based control design procedure; 2) network connectivity during dynamic obstacle avoidance is preserved by constructing the auxiliary signals; and 3) owing to neural networks-based compensating variables, the bounding conditions of time derivatives of virtual controllers are not required in the stability analysis.

Distributed Adaptive Fault-Tolerant Formation-Containment Control With Prescribed Performance for Heterogeneous Multiagent Systems

This article proposes a distributed adaptive fault-tolerant formation-containment control with prescribed performance for heterogeneous multiagent systems (MASs) consisting of multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) in the presence of actuator faults. First, utilizing the neighborhood formation error information, the distributed fault-tolerant formation control strategy is developed for the trajectory dynamics of each UAV to achieve the formation tracking, that is, all UAVs track the virtual leader and perform the prespecified formation configuration. Then, the adaptive fault-tolerant containment algorithm, independent of the positions of the leaders, is proposed to guarantee the UGVs converge to the convex hull formed by the leader UAVs. The adaptive estimation scheme is constructed to compensate for the unknown system parameters and actuator loss-of-effectiveness and bias faults. The formation-containment tracking performance is analyzed based on Lyapunov theory with the synchronization errors satisfying the prescribed performance. A simulation example based on UAVs-UGVs systems is adopted to verify the effectiveness of the proposed control strategy.

Observer-Based Event-Triggered Adaptive Control for Nonlinear Multiagent Systems With Unknown States and Disturbances

Based on radial basis function neural networks (RBF NNs) and backstepping techniques, this brief considers the consensus tracking problem for nonlinear semi-strict-feedback multiagent systems with unknown states and disturbances. The adaptive event-triggered control scheme is introduced to decrease the update times of the controller so as to save the limited communication resources. To detect the unknown state, external disturbance, and reduce calculation workload, the state observer and disturbance observer as well as the first-order filter are first jointly constructed. It is shown that all the output signals of followers can uniformly track the reference signal of the leader and all the error signals are uniformly bounded. A simulation example is carried out to further prove the effectiveness of the proposed control scheme.

Distributed Fuzzy Optimal Consensus Control of State-Constrained Nonlinear Strict-Feedback Systems

This article investigates the distributed fuzzy optimal consensus control problem for state-constrained nonlinear strict-feedback systems under an identifier-actor-critic architecture. First, a fuzzy identifier is designed to approximate each agent's unknown nonlinear dynamics. Then, by defining multiple barrier-type local optimal performance indexes for each agent, the optimal virtual and actual control laws are obtained, where two fuzzy-logic systems working as the actor network and critic network are used to execute control behavior and evaluate control performance, respectively. It is proved that the proposed control protocol can drive all agents to reach consensus without violating state constraints, and make the local performance indexes reach the Nash equilibrium simultaneously. Simulation studies are given to verify the effectiveness of the developed fuzzy optimal consensus control approach.

Adaptive Event-Triggered Sliding-Mode Control for Consensus Tracking of Nonlinear Multiagent Systems With Unknown Perturbations

The adaptive tracking control problem of leader-following nonlinear multiagent systems (MASs) subject to unknown perturbations and limited network bandwidth is investigated by the robust adaptive event-triggered sliding-mode control method. A distributed integral sliding mode is established to realize the finite-time reachability of the states of the leader-following nonlinear MAS. An adaptive triggering control mechanism is then put forward to dynamically adjust the triggering interval, thus reducing the actuator wear and unnecessary network resource consumption. The positions and velocities of the leader-following nonlinear MAS subject to unknown external disturbances are, respectively, driven to the equilibrium point by constructing a distributed event-based robust adaptive sliding-mode protocol. Via the Lyapunov stability theory and Barbalat lemma, sufficient conditions to ensure the adaptive tracking performance are derived for leader-following nonlinear MASs. Three simulation examples to verify the efficacy of the proposed event-based robust adaptive sliding-mode controller design are presented.

Adaptive-observer-based consensus tracking with fault-tolerant network connectivity of uncertain time-delay nonlinear multiagent systems with actuator and communication faults

In this study, a distributed output-feedback design approach for ensuring fault-tolerant initial network connectivity and preselected-time consensus tracking performance is proposed for a class of uncertain time-delay nonlinear multiagent systems (TDNMSs) with unexpected actuator and communication faults. It is assumed that time-varying state delays and system nonlinearities in TDNMSs are unknown. The main contribution of this study is to provide a delay-independent output-feedback control strategy to address a fault-tolerant initial connectivity preservation problem in the consensus tracking field. A local delay-independent adaptive state observer using neural networks is designed for each follower, and the boundedness of local observation errors is proved by constructing a Lyapunov-Krasovskii functional and adaptive tuning laws. Then, the local nonlinear relative output errors using a time-varying function with a preselected convergence time are derived to design simple local delay-independent trackers. The stability of the proposed consensus tracking system is analyzed, and simulation comparison results demonstrate the validity of the proposed strategy.

Leader-Follower Formation Learning Control of Discrete-Time Nonlinear Multiagent Systems

This article investigates the leader-follower formation learning control (FLC) problem for discrete-time strict-feedback multiagent systems (MASs). The objective is to acquire the experience knowledge from the stable leader-follower adaptive formation control process and improve the control performance by reusing the experiential knowledge. First, a two-layer control scheme is proposed to solve the leader-follower formation control problem. In the first layer, by combining adaptive distributed observers and constructed i_n -step predictors, the leader's future state is predicted by the followers in a distributed manner. In the second layer, the adaptive neural network (NN) controllers are constructed for the followers to ensure that all the followers track the predicted output of the leader. In the stable formation control process, the NN weights are verified to exponentially converge to their optimal values by developing an extended stability corollary of linear time-varying (LTV) system. Second, by constructing some specific "learning rules," the NN weights with convergent sequences are synthetically acquired and stored in the followers as experience knowledge. Then, the stored knowledge is reused to construct the FLC. The proposed FLC method not only solves the leader-follower formation problem but also improves the transient control performance. Finally, the validity of the presented FLC scheme is illustrated by simulations.

Full Information Control for Switched Neural Networks Subject to Fault and Disturbance

The article investigates full information control problem for switched neural networks subject to fault and disturbance. First, the main objective is realizing interval stability and zero tracking error under condition that neither of the neuron states' vectors including the plant and reference models is available. Second, the desired full information controller and neural networks' observer are designed to ensure observer-based dynamic error system mean-square exponentially stable with sufficient condition of strict weight H_∞ /H_- performance levels. Finally, we concentrate on stability analyses and fault tolerance for switched neural networks with fault accompanied by disturbance through linear matrix inequalities (LMIs), Lyapunov function, and average dwell time, discussing it according to different values of fault. Finally, simulation examples are listed to account for the availability and effectiveness of the research methodology.

Neural-Network-Based Adaptive Tracking Control for Nonlinear Multiagent Systems: The Observer Case

This article focuses on the neural-network (NN)-based adaptive tracking control issue for a class of high-order nonlinear multiagent systems both subjected to the immeasurable state variables and unknown external disturbance. Combining with the radial basis function NNs (RBF NNs), the composite disturbance observer and state observer for each follower are established, respectively. The purpose of this work is to develop NN-based adaptive tracking control schemes such that the output of each follower ultimately tracks that of the leader and all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded by utilizing the backstepping technique. Furthermore, so as to cope with the sparsity of the control resources, the proposed method is extended to the event-triggered case and the adaptive event-triggered tracking control protocol is formulated for nonlinear multiagent systems. Finally, the numerical example is performed to verify the efficacy of the proposed approach.

Neural-Network-Based Distributed Asynchronous Event-Triggered Consensus Tracking of a Class of Uncertain Nonlinear Multi-Agent Systems

This article proposes a neural-network-based adaptive asynchronous event-triggered design strategy for the distributed consensus tracking of uncertain lower triangular nonlinear multi-agent systems under a directed network. Compared with the existing event-triggered recursive consensus tracking designs using multiple neural networks for each follower and continuous communications among followers, the primary contribution of this study is the development of an asynchronous event-triggered consensus tracking methodology based on a single-neural network for each follower under event-driven intermittent communications among followers. To this end, a distributed event-triggered estimator using neighbors' triggered output information is developed to estimate a leader signal. Subsequently, the estimated leader signal is used to design local trackers. Only a triggering law and a single-neural network are used to design the local tracking law of each follower, irrespective of unmatched unknown nonlinearities. The information of each follower and its neighbors is asynchronously and intermittently communicated through a directed network. Thus, the proposed asynchronous event-triggered tracking scheme can save communicational and computational resources. From the Lyapunov stability theorem, the stability of the entire closed-loop system is analyzed and the comparative simulation results demonstrate the effectiveness of the proposed control strategy.

Distributed Quantized Feedback Design Strategy for Adaptive Consensus Tracking of Uncertain Strict-Feedback Nonlinear Multiagent Systems With State Quantizers

This study investigates a quantized feedback design problem for distributed adaptive leader-following consensus of uncertain strict-feedback nonlinear multiagent systems with state quantizers. It is assumed that all system nonlinearities of followers are unknown and heterogeneous, all state variables of each follower are quantized by a uniform state quantizer, and quantized states of followers are only communicated under a directed network. Compared with previous approximation-based distributed consensus tracking methods for uncertain lower triangular multiagent systems, the main contribution of this article is addressing the distributed quantized state communication problem in the adaptive leader-following consensus tracking field of uncertain lower triangular multiagent systems. A quantized-states-based local adaptive control law for each follower is derived by designing quantized-signals-based weight tuning laws for neural-network-based function approximators. By analyzing the boundedness of the local quantization errors, it is shown that the total closed-loop signals are uniformly ultimately bounded and the consensus tracking errors converge to a sufficiently small domain around the origin. Finally, simulation examples, including multiple ship steering systems, are considered to verify the effectiveness of the proposed theoretical approach.

Observer-Based Adaptive Synchronization of Multiagent Systems With Unknown Parameters Under Attacks

This article studies the observer-based adaptive synchronization of multiagent systems (MASs) with unknown parameters under attacks. First, to estimate the state of agents, the observer for MAS is introduced. When disturbance, nonlinear function, and system model uncertainty are not considered, the nominal controller is proposed to achieve synchronization and state estimation. Then, in order to eliminate the effect of unknown parameters in the disturbance, nonlinear function, and system model uncertainty, the adaptive controller with switching term is introduced. However, the attack will lead to the destruction of the network topology so as the destruction of the nominal controller. By constructing an appropriate Lyapunov function, we analyze the effect caused by attacks, and the security control law is given to make sure the synchronization of the MASs under attacks. Finally, a numerical simulation is given to verify the validness of the obtained theorem.

Distributed Fuzzy Adaptive Output-Feedback Control of Unknown Nonlinear Multiagent Systems in Strict-Feedback Form

This article is concerned with the cooperative tracking control problem for heterogeneous multiagent systems in a leader-following form under a directed graph. The dynamics of each following agent is unknown, obeying a strict-feedback form. With the help of fuzzy-logic systems, input filters, and constraint-handling schemes, a fully distributed output-feedback control algorithm is proposed to achieve output synchronization with prescribed performance and guarantee boundedness of signals in the closed-loop systems. In addition, the algorithm exhibits a simplicity control attribute in the sense that: 1) the control design utilizes only relative output measurements, and no extra information needs to be transmitted via the network and 2) the issue of explosion of complexity is addressed, without employing command filters or dynamic surface control techniques. Finally, the simulation results clarify and verify the established theoretical findings.

Adaptive Finite-Time Containment Control of Uncertain Multiple Manipulator Systems

This article is concerned with the containment control of multiple manipulators with uncertain parameters. A novel distributed adaptive backstepping strategy is given in the finite-time control framework. The finite-time command filters (FTCFs) used in the strategy can avoid the explosion of complexity problem for conventional backstepping. To further improve the control performance, the filtering errors caused by the used FTCFs are removed by using the error compensation mechanism (ECM). The proposed virtual control signal, the control torque, and the adaptive updating law can guarantee the set tracking errors converge to an adjustable neighborhood of the origin in finite time in the presence of uncertain parameters. Because the virtual control signal and ECM only use the local information, the established method is completely distributed. Two simulation examples are given to show the effectiveness of the proposed scheme.

Consensus Tracking Control of Uncertain Multiagent Systems With Sampled Data and Time-Varying Delay

In this article, the adaptive consensus tracking control is developed for uncertain multiagent systems with time-varying state delay in the case that leader's state is accessible at sampling instants. By proposing a distributed sampled observer with hybrid form, adaptive tracking controller with the complementary term is designed for first-order multiagent systems, and then is extended to high-order multiagent systems with the aid of dynamic surface control. Through the complementary term, the effects of parameter estimation error as well as dynamical terms with time-varying delays are eliminated and thus less conservative condition on time delays is required. It is proved that, under criteria in terms of linear matrix inequalities (LMIs), tracking error and estimation error exponentially converge to zero for first-order systems, and to a sufficiently small neighborhood of zero for high-order systems.

Distributed Adaptive Control for Asymptotically Consensus Tracking of Uncertain Nonlinear Systems With Intermittent Actuator Faults and Directed Communication Topology

In this article, we investigate the output consensus tracking problem for a class of high-order nonlinear systems with unknown parameters, uncertain external disturbances, and intermittent actuator faults. Under the directed topology conditions, a novel distributed adaptive controller is proposed. The common time-varying trajectory is allowed to be totally unknown by part of subsystems. Therefore, the assumption on the linearly parameterized trajectory signal in most literature is no longer needed. To achieve the relaxation, extra distributed parameter estimators are introduced in all subsystems. Besides, to handle the actuator faults occurring at possibly infinite times, a new adaptive compensation technique is adopted. It is shown that with the proposed scheme, all closed-loop signals are globally uniformly bounded and asymptotically output consensus tracking can be achieved.

Finite-Time Tracking Control for Nonlinear Systems via Adaptive Neural Output Feedback and Command Filtered Backstepping

This article is concerned with the tracking control problem for uncertain high-order nonlinear systems in the presence of input saturation. A finite-time control strategy combined with neural state observer and command filtered backstepping is proposed. The neural network models the unknown nonlinear dynamics, the finite-time command filter (FTCF) guarantees the approximation of its output to the derivative of virtual control signal in finite time at the backstepping procedure, and the fraction power-based error compensation system compensates for the filtering errors between FTCF and virtual signal. In addition, the input saturation problem is dealt with by introducing the auxiliary system. Overall, it is shown that the designed controller drives the output tracking error to the desired neighborhood of the origin at a finite time and all the signals in the closed-loop system are bounded at a finite time. Two simulation examples are given to demonstrate the control effectiveness.

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.

Adaptive Consensus Tracking Control of Uncertain Nonlinear Multiagent Systems With Predefined Accuracy

In this article, we consider the leader-follower consensus control problem of uncertain multiagent systems, aiming to achieve the improvement of system steady state and transient performance. To this end, a new adaptive neural control approach is proposed with a novel design of the Lyapunov function, which is generated with a class of positive functions. Guided by this idea, a series of smooth functions is incorporated into backstepping design and Lyapunov analysis to develop a performance-oriented controller. It is proved that the proposed controller achieves a perfect asymptotic consensus performance and a tunable L₂ transient performance of synchronization errors, whereas most existing results can only ensure the stability. Simulation demonstrates the obtained results.

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.

Cooperative Adaptive Output Regulation for Lower Triangular Nonlinear Multi-Agent Systems Subject to Jointly Connected Switching Networks

The cooperative global robust output regulation problem for multi-agent systems is a generalization of the leader-following consensus problem. The problem has been studied for various multi-agent systems over connected static networks and for some special classes of nonlinear multi-agent systems over jointly connected switching networks. In this paper, we further consider the same problem for a class of heterogeneous lower triangular nonlinear multi-agent systems over jointly connected switching networks. This class of systems is quite general in that it contains inverse dynamics, is of any order, and its subsystems can have different relative degrees. We will integrate the adaptive distributed observer and the distributed internal model approach to come up with a recursive approach to deal with our problem. We will also apply our approach to a leader-following consensus problem for a group of hyperchaotic Lorenz systems.

Distributed Adaptive Neural Network Control Applied to a Formation Tracking of a Group of Low-Cost Underwater Drones in Hazardous Environments

This paper addresses a formation tracking problem of multiple low-cost underwater drones by implementing distributed adaptive neural network control (DANNC). It is based on a leader-follower architecture to operate in hazardous environments. First, unknown parameters of underwater vehicle dynamics, which are important requirements for real-world applications, are approximated by a neural network using a radial basis function. More specifically, those parameters are only calculated by local information, which can be obtained by an on-board camera without using an external positioning system. Secondly, a potential function is employed to ensure there is no collision between the underwater drones. We then propose a desired configuration of a group of unmanned underwater vehicles (UUVs) as a time-variant function so that they can quickly change their shape between them to facilitate the crossing in a narrow area. Finally, three UUVs, based on a robot operating system (ROS) platform, are used to emphasize the realistic low-cost aspect of underwater drones. The proposed approach is validated by evaluating in different experimental scenarios.

Distributed Control of High-Order Nonlinear Input Constrained Multiagent Systems Using a Backstepping-Free Method

This paper presents novel cooperative tracking control for a class of input-constrained multiagent systems with a dynamic leader. Each follower agent is described by a high-order nonlinear dynamics in strict feedback form with input constraints. Our main contribution lies in presenting a system transformation method that can convert the input-constrained state feedback cooperative tracking control of agents into an unconstrained output feedback control of agents with dynamics in Brunovsky normal form. As a result, the original problem is simplified to be a simple stabilization of the transformed system for the agents. Thus, the use of the backstepping scheme is obviated, and the synthesis and computation are extremely simplified. It is strictly proved that all follower agents can synchronize to the leader with bounded synchronization errors, and all other signals in the closed-loop system are semi-global uniformly ultimately bounded. Finally, numerical analysis is carried out to validate the theoretical results and demonstrate the effectiveness of the proposed approach.

Distributed adaptive neural networks leader-following formation control for quadrotors with directed switching topologies

The leader-following formation problem is discussed for a team of quadrotors under directed switching topologies. To obtain a more general dynamic model, we describe the quadrotor system in a non-affine pure-feedback form with mismatched unknown nonlinearities. By employing an adaptive neural networks state observer to approximate the unknown nonlinear functions and to reconstruct the immeasurable inner states, we propose a novel distributed output feedback formation control protocol with the backstepping method combining with the dynamic surface control technique. From the Lyapunov stability theorem, all signals in the closed-loop formation system are proven to be cooperatively semiglobally uniformly ultimately bounded for any given bounded initial conditions. Finally, we proved that we verify the performance of the proposed formation control approach by a simulation study.

Consensus Maneuvering for a Class of Nonlinear Multivehicle Systems in Strict-Feedback Form

In this paper, a consensus maneuvering problem for nonlinear multivehicle systems in strict-feedback form is investigated. The consensus maneuvering problem includes a geometric task and a dynamic task. The geometric task means that all trajectories of follower vehicles converge to a parameterized path. The dynamic task is to drive the system to satisfy a desired dynamic assignment. A consensus maneuvering controller is developed for each vehicle based on a modular design approach. First, an estimator module is designed based on an echo state network, which is used to estimate uncertain nonlinearities. Then, a controller module is designed based on a modified dynamic surface control method through the use of a second-order nonlinear tracking differentiator. Finally, a path update law is designed based on a distributed maneuvering error feedback and a filtering scheme. The proposed controller is distributed in the sense that the path information is accessed by a small number of follower vehicles only. The stability of the closed-loop system cascaded by the estimator module and the controller module is analyzed based on input-to-state stability theory and cascade theory. Simulation results are provided to demonstrate the efficacy of the proposed consensus maneuvering controllers for uncertain nonlinear strict-feedback systems.

Adaptive Neural Dynamic Surface Control for Nonstrict-Feedback Systems With Output Dead Zone

This paper focuses on the problem of adaptive output-constrained neural tracking control for uncertain nonstrict-feedback systems in the presence of unknown symmetric output dead zone and input saturation. A Nussbaum-type function-based dead-zone model is introduced such that the dynamic surface control approach can be used for controller design. The variable separation technique is employed to decompose the unknown function of entire states in each subsystem into a series of smooth functions. Radial basis function neural networks are utilized to approximate the unknown black-box functions derived from Young's inequality. With the help of auxiliary first-order filters, the dimensions of neural network input are reduced in each recursive design. A main advantage of the proposed method is that for an -order nonlinear system, only one adaptation parameter needs to be tuned online. It is rigorously shown that the proposed output-constrained controller guarantees that all the closed-loop signals are semiglobal uniformly ultimately bounded and the tracking error never violates the output constraint.

Command filter based adaptive fuzzy bipartite output consensus tracking of nonlinear coopetition multi-agent systems with input saturation

This paper is concerned with the adaptive bipartite output consensus tracking problem of high-order nonlinear coopetition multi-agent systems with input saturation under a signed directed graph. A distributed fuzzy-based command filtered backstepping scheme is proposed, where the unknown nonlinear dynamics are approximated by the fuzzy logic system (FLS). The errors compensation mechanism is constructed to eliminate the errors caused by filters. Under the proposed control scheme, we only need to design one adaptive law for each agent, and it is proved that the bipartite output tracking errors converge into the desired neighborhood and all the closed-loop signals are bounded although the input saturation exists. Two numerical examples are included to verify the effectiveness of given scheme.