Distributed Sliding-Mode Tracking Control of Second-Order Nonlinear Multiagent Systems: An Event-Triggered Approach

Dynamic Protocol-Based Control for Hidden Stochastic Jump Multiarea Power Systems in Finite-Time Interval

A dynamic event-triggered load frequency control (LFC) is studied for interconnected multiarea power systems (IMAPSs) with stochastic semi-Markov parameters from the perspective of finite-time interval. To facilitate the sudden changes, the underlying semi-Markov process (SMP) is adopted to characterize the random behavior of IMAPSs. A dynamic event-triggered protocol (DETP) is developed to modulate the transmission frequency while maintaining predefined system performance. Owing to complicated grid environment, the hidden semi-Markov model (HSMM) is proposed to solve the asynchronization between the system mode and the controller mode, which forms a new asynchronous mechanism to better understand the behavior pattern of the system. The novelty of this article is to construct a suitable asynchronous control strategy to solve the mismatch between the system mode and the controller mode under the framework of IMAPSs. Different from static event-triggered protocol (ETP), the DETP is proposed, in which the threshold parameters can be dynamically adjusted to reduce the waste of communication resources and achieve dynamic performance in limited time. According to the stochastic system theory and the finite-time theory, by constructing a modular dependent random Lyapunov function, sufficient conditions are obtained to ensure the finite-time boundedness of the corresponding system with performance. Finally, the efficiency is demonstrated through three-area power systems.

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.

Predefined-time distributed optimization and anti-disturbance control for nonlinear multi-agent system with neural network estimator: A hierarchical framework

This paper addresses the predefined-time distributed optimization of nonlinear multi-agent system using a hierarchical control approach. Considering unknown nonlinear functions and external disturbances, we propose a two-layer hierarchical control framework. At the first layer, a predefined-time distributed estimator is employed to produce optimal consensus trajectories. At the second layer, a neural-network-based predefined-time disturbance observer is introduced to estimate the disturbance, with neural networks used to approximate the unknown nonlinear functions. A neural-network-based anti-disturbance sliding mode control mechanism is presented to ensure that the system trajectories can track the optimal trajectories within a predefined time. The feasibility of this hierarchical control framework is verified by utilizing the Lyapunov method. Numerical simulations are conducted separately using models of robotic arms and mobile robots to validate the effectiveness of the proposed method.

PD and PI Control for the Lag Consensus of Nonlinear Multiagent Systems With and Without External Disturbances

In this article, we investigate the lag consensus and lag H∞ consensus problems for second-order nonlinear multiagent systems (MASs) by utilizing the proportional-derivative (PD) and proportional-integral (PI) control methods. On the one hand, a criterion is developed for ensuring the lag consensus of the MAS by choosing an appropriate PD control protocol. Moreover, a PI controller is also provided to guarantee that the MAS can achieve lag consensus. On the other hand, several lag H∞ consensus criteria are also given for the case in which external disturbances appear in the MAS; these criteria are developed by exploiting the PD and PI control strategies. Finally, the devised control schemes and the developed criteria are verified by employing two numerical examples.

Data-Driven Optimal Bipartite Consensus Control for Second-Order Multiagent Systems via Policy Gradient Reinforcement Learning

This article investigates the optimal bipartite consensus control (OBCC) problem for unknown second-order discrete-time multiagent systems (MASs). First, the coopetition network is constructed to describe the cooperative and competitive relationships between agents, and the OBCC problem is proposed by the tracking error and related performance index function. Based on the distributed policy gradient reinforcement learning (RL) theory, a data-driven distributed optimal control strategy is obtained to guarantee the bipartite consensus of all agents' position and velocity states. In addition, the offline data sets ensure the learning efficiency of the system. These data sets are generated by running the system in real time. Besides, the designed algorithm is an asynchronous version, which is essential to solve the challenge caused by the computational ability difference between nodes in MASs. Then, by means of the functional analysis and Lyapunov theory, the stability of the proposed MASs and the convergence of the learning process are analyzed. Furthermore, an actor-critic structure containing two neural networks is used to implement the proposed methods. Finally, a numerical simulation shows the effectiveness and validity of the results.

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.

Secure control for remote networked stochastic systems via integral sliding mode

This paper deals with the secure control problem for a class of networked stochastic systems with false data injection attacks via an integral sliding mode control technique. The networked control system is with a hierarchical structure, and the main controller and a remote controller are considered to realize the secure control against false data injection attacks on the network between a main controller and the plant. A mode-shared event-triggering controller is designed as the main controller, by utilizing a time delay approach. An input-output model based on a two-term approximation is applied to cope with the formulated time-varying delay. Then, the scaled small gain theory is employed to analyze the stability of the resulting system. Sufficient conditions on ensuring the desired system performance are derived and then the controller parameters are synthesized. Moreover, an elaborated sliding mode control law is proposed for the desired secure control action. Finally, two simulation examples are permitted to verify the effectiveness of the theoretical derivations.

Event-Based Finite-Time Neural Control for Human-in-the-Loop UAV Attitude Systems

This article focuses on the event-based finite-time neural attitude consensus control problem for the six-rotor unmanned aerial vehicle (UAV) systems with unknown disturbances. It is assumed that the six-rotor UAV systems are controlled by a human operator sending command signals to the leader. A disturbance observer and radial basis function neural networks (RBF NNs) are applied to address the problems regarding external disturbances and uncertain nonlinear dynamics, respectively. In addition, the proposed finite-time command filtered (FTCF) backstepping method effectively manages the issue of "explosion of complexity," where filtering errors are eliminated by the error compensation mechanism. In addition, an event-triggered mechanism is considered to alleviate the communication burden between the controller and the actuator in practice. It is shown that all signals of the six-rotor UAV systems are bounded and the consensus errors converge to a small neighborhood of the origin in finite time. Finally, the simulation results demonstrate the effectiveness of the proposed control scheme.

Adaptive Neural Coordinated Control for Multiple Euler-Lagrange Systems With Periodic Event-Triggered Sampling

This article addresses the event-triggered coordinated control problem for multiple Euler-Lagrange systems subject to parameter uncertainties and external disturbances. Based on the event-triggered technique, a distributed coordinated control scheme is first proposed, where the neural network-based estimation method is incorporated to compensate for parameter uncertainties. Then, an input-based continuous event-triggered (CET) mechanism is developed to schedule the triggering instants, which ensures that the control command is activated only when some specific events occur. After that, by analyzing the possible finite-time escape behavior of the triggering function, the real-time data sampling and event monitoring requirement in the CET strategy is tactfully ruled out, and the CET policy is further transformed into a periodic event-triggered (PET) one. In doing so, each agent only needs to monitor the triggering function at the preset periodic sampling instants, and accordingly, frequent control updating is further relieved. Besides, a parameter selection criterion is provided to specify the relationship between the control performance and the sampling period. Finally, a numerical example of attitude synchronization for multiple satellites is performed to show the effectiveness and superiority of the proposed coordinated control scheme.

Fully Distributed Event-Driven Adaptive Consensus of Unknown Linear Systems

This article considers the consensus problem of unknown linear multiagent systems (MASs) through adaptive event-driven control in leader-follower and leaderless networks. The proposed event-driven algorithms do not involve any global information related to the network communication structure and rely only on local information exchange to achieve consensus on MASs and are therefore fully distributed. Furthermore, the constraint of continuous communication among the agents is eliminated in terms of control law updates and triggering state monitoring. Another desirable aspect of this article is that the design process of the control algorithms is independent of the parameters of each agent's dynamics and thus does not require precise information about the dynamics of MASs. We further exclude the Zeno behavior of each agent by proving the existence of a strict positive lower bound between any two adjacent events. Finally, the effectiveness of the proposed adaptive event-driven algorithms is verified by a simulation example.

Composite control of anti-drone platform for stable tracking under disturbance

First, focused on the complex problem that a U-shaped tracking frame is unreachable to obtain the pointing angles of an unmanned aerial vehicle target, a novel coordinate transformation method is proposed in this paper. The fixed transformation relationship between the intermediate links is deduced by establishing a unified coordinate system, simplifying the algorithm conversion process, and saving computing resources and time. Furthermore, the accuracy of the proposed method has been verified in both aspects of theory and experiment. Then, in order to achieve smooth motion performance between target pointing strategy and stable tracking strategy, a mode switching method based on hysteresis intervals is developed. Compared with the traditional single-point threshold method, the switching method overcomes the high frequency jitter problem. The experimental results validate the consistency between practical effects and theoretical expectations. Finally, to improve the disturbance rejection performance of the platform, a composite control method integrating the information from the gyroscope and circular grating is proposed. The corresponding control scheme and the compensation principle are conceived and explained. The experimental results show the anti-interference performance of the proposed composite control method is five times that of the closed-loop method based on the gyroscope speed signal and two times that of the disturbance observer control method.

Disturbance observer-based fuzzy event-triggered ISMC design: Tracking performance

This article presents a disturbance observer (DO)-based event-triggered integral sliding mode tracking control (ISMTC) for continuous-time Takagi-Sugeno (T-S) fuzzy model (TSFM) subject to external disturbances. Merging the event-triggered control (ETC) with integral sliding mode control (ISMC) approach is led to reach the better accommodate the features of ISMC. To do this, two forms of fuzzy integral sliding surfaces (FISSs) are proposed. The first is the periodic-time-based FISS that is presented to provide the robustness of the tracking performance from the initial moment. The second is the event-triggered-based FISS which is proposed to obtain the fuzzy event-triggered ISMTC law. To more decrease the chattering effects and compensate the tracking performance against the disturbances, a fuzzy disturbance observer (FDO) is proposed to estimate the mismatched disturbances. Compared with the existing works, a more practical controller is proposed based on the asynchronous premise variables. Utilizing the common quadratic Lyapunov function, appropriate conditions are derived to verify that the tracking error is robust from the initial moment. Furthermore, by adopting a decaying triggering threshold, it is guaranteed that the system is Zeno-free during the process. To verify the effectiveness of the suggested event-triggered ISMTC, a practical system including continuous stirred tank reactor (CSTR) is simulated and the results are compared.

Event-Triggered Control for Markov Jump Systems Subject to Mismatched Modes and Strict Dissipativity

In order to save network resources of discrete-time Markov jump systems, an event-triggered control framework is employed in this article. The threshold parameter in the event-triggered mechanism is designed as a diagonal matrix in which all elements can be adjusted according to system performance requirements. The hidden Markov model is introduced to characterize the asynchronization between the controller and controlled system. The effect of randomly occurring gain fluctuations is taken into account during the controller design. For the purpose of guaranteeing that the closed-loop system is stochastically stable and satisfies the strictly (D₁,D₂,D₃)-γ- dissipative performance, sufficient conditions are constructed by employing the Lyapunov function and stochastic analysis. After linearization, the proposed controller gains are obtained by solving the linear matrix inequalities. Ultimately, a practical example of the dc motor device is used to illustrate the effectiveness of the proposed new design technique.

Event-Triggered Multigradient Recursive Reinforcement Learning Tracking Control for Multiagent Systems

In this article, the tracking control problem of event-triggered multigradient recursive reinforcement learning is investigated for nonlinear multiagent systems (MASs). Attention is focused on the distributed reinforcement learning approach for MASs. The critic neural network (NN) is applied to estimate the long-term strategic utility function, and the actor NN is designed to approximate the uncertain dynamics in MASs. The multigradient recursive (MGR) strategy is tailored to learn the weight vector in NN, which eliminates the local optimal problem inherent in gradient descent method and decreases the dependence of initial value. Furthermore, reinforcement learning and event-triggered mechanism can improve the energy conservation of MASs by decreasing the amplitude of the controller signal and the controller update frequency, respectively. It is proved that all signals in MASs are semiglobal uniformly ultimately bounded (SGUUB) according to the Lyapunov theory. Simulation results are given to demonstrate the effectiveness of the proposed strategy.

Stable Spinning Deployment Control of a Triangle Tethered Formation System

The tethered formation system has been widely studied due to its extensive use in aerospace engineering, such as Earth observation, orbital location, and deep space exploration. The deployment of such a multitethered system is a problem because of the oscillations and complex formation maintenance caused by the space tether's elasticity and flexibility. In this article, a triangle tethered formation system is modeled, and an exact stable condition for the system's maintaining is carefully analyzed, which is given as the desired trajectories; then, a new control scheme is designed for its spinning deployment and stable maintenance. In the proposed scheme, a novel second-order sliding mode controller is given with a designed nonsingular sliding-variable. Based on the theoretical proof, the addressed sliding variable from the arbitrary initial condition can converge to the manifold in finite time, and then sliding to the equilibrium in finite time as well. The simulation results show that compared with classic second sliding-mode control, the proposed scheme can speed up the convergence of the states and sliding variables.

Uncertainty Compensator and Fault Estimator-Based Exponential Supertwisting Sliding-Mode Controller for a Mobile Robot

This work proposes a novel event-triggered exponential supertwisting algorithm (ESTA) for path tracking of a mobile robot. The proposed work is divided into three parts. In the first part, a fractional-order sliding surface-based exponential supertwisting event-triggered controller has been proposed. Fractional-order sliding surface improves the transient response, and the exponential supertwisting reaching law reduces the reaching phase time and eliminates the chattering. The event-triggering condition is derived using the Lipschitz method for minimum actuator utilization, and the interexecution time between two events is derived. In the second part, a fault estimator is designed to estimate the actuator fault using the Lyapunov stability theory. Furthermore, it is shown that in the presence of matched and unmatched uncertainty, event-trigger-based controller performance degrades. Hence, in the third part, an integral sliding-mode controller (ISMC) has been clubbed with the event-trigger ESTA for filtering of the uncertainties. It is also shown that when fault estimator-based ESTA is clubbed with ISMC, then the robustness of the controller increases, and the tracking performance improves. This novel technique is robust toward uncertainty and fault, offers finite-time convergence, reduces chattering, and offers minimum resource utilization. Simulations and experimental studies are carried out to validate the advantages of the proposed controller over the existing 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.

Event-Driven Connectivity-Preserving Coordinated Control for Multiple Spacecraft Systems With a Distance-Dependent Dynamic Graph

This article considers the connectivity preservation coordinated control problem for multiple spacecraft systems subject to limited communication resources and sensing capability. By constructing a novel bump function, a distance-dependent dynamic communication network model is first presented, which characterizes the interaction strength as a nonlinear smooth function varying with the relative distance of spacecraft continuously. Subsequently, based on an edge-tension potential function, a distributed event-driven coordinated control scheme is proposed to achieve formation consensus, while ensuring that adjacent spacecraft is always within the allowable connectivity range. Meanwhile, to avoid redundant data transmissions, a hybrid dynamic event-triggered mechanism with maximum triggering interval is developed to schedule the communication frequency among spacecraft. It is proven that the onboard communication resources occupation can be reduced significantly and the Zeno phenomenon is strictly excluded. Finally, the efficiency of the proposed method for, as an example, four-spacecraft formation system is substantiated.

Event-Triggered Resilient L∞ Control for Markov Jump Systems Subject to Denial-of-Service Jamming Attacks

In this article, the event-triggered resilient L_∞ control problem is concerned for the Markov jump systems in the presence of denial-of-service (DoS) jamming attacks. First, a fixed lower bound-based event-triggering scheme (ETS) is presented in order to avoid the Zeno problem caused by exogenous disturbance. Second, when DoS jamming attacks are involved, the transmitted data are blocked and the old control input is kept by using the zero-order holder (ZOH). On the basis of this process, the effect of DoS attacks on ETS is further discussed. Next, by utilizing the state-feedback controller and multiple Lyapunov functions method, some criteria incorporating the restriction of DoS jamming attacks are proposed to guarantee the L_∞ control performance of the event-triggered Markov closed-loop jump system. In particular, the bounded transition rates rather than the exact ones are taken into account. That is appropriate for the practical environment in which transition rates of the Markov process are difficult to measure accurately. Correspondingly, some criteria are proposed to obtain state-feedback gains and event-triggering parameters simultaneously. Finally, we provide two examples to show the effectiveness of the proposed method.

Fuzzy Adaptive Cooperative Consensus Tracking of High-Order Nonlinear Multiagent Networks With Guaranteed Performances

This work addresses the distributed consensus tracking problem for an extended class of high-order nonlinear multiagent networks with guaranteed performances over a directed graph. The adding one power integrator methodology is skillfully incorporated into the distributed protocol so as to tackle high powers in a distributed fashion. The distinguishing feature of the proposed design, besides guaranteeing closed-loop stability, is that some transient-state and steady-state metrics (e.g., maximum overshoot and convergence rate) can be preselected a priori by devising a novel performance function. More precisely, as opposed to conventional prescribed performance functions, a new asymmetry local tracking error-transformed variable is designed to circumvent the singularity problem and alleviate the computational burden caused by the conventional transformation function and its inverse function, and to solve the nondifferentiability issue that exists in most existing designs. Furthermore, the consensus tracking error is shown to converge to a residual set, whose size can be adjusted as small as desired through selecting proper parameters, while ensuring closed-loop stability and preassigned performances. One numerical and one practical example have been conducted to highlight the superiority of the proposed strategy.

Extended Dissipative Sliding-Mode Control for Discrete-Time Piecewise Nonhomogeneous Markov Jump Nonlinear Systems

This article analyzes the problem of the sliding-mode control (SMC) design for discrete-time piecewise nonhomogeneous Markov jump nonlinear systems (MJNSs) subject to an external disturbance with time-varying transition probabilities (TPs). A discrete-time asynchronous integral sliding surface is constructed, which yields matched-nonlinearity-free sliding-mode dynamics (SMDs). Then, by using the mode-dependent Lyapunov function technique, a sufficient condition is established for ensuring the stochastic stability of SMD with extended dissipation. The solution to designing controller gains is obtained. Moreover, an SMC law and an adaptive law are, respectively, derived for driving the system trajectories to move into a predetermined sliding-mode region with specified precision. Finally, the feasibility and effectiveness of the new design are verified and demonstrated by a simulation example.

Adaptive Finite-Time Fault-Tolerant Control for Uncertain Flexible Flapping Wings Based on Rigid Finite Element Method

The bionic flapping-wing robotic aircraft is inspired by the flight of birds or insects. This article focuses on the flexible wings of the aircraft, which has great advantages, such as being lightweight, having high flexibility, and offering low energy consumption. However, flexible wings might generate the unexpected deformation and vibration during the flying process. The vibration will degrade the flight performance, even shorten the lifespan of the aircraft. Therefore, designing an effective control method for suppressing vibrations of the flexible wings is significant in practice. The main purpose of this article is to develop an adaptive fault-tolerant control scheme for the flexible wings of the aircraft. Dynamic modeling, control design, and stability verification for the aircraft system are conducted. First, the dynamic model of the flexible flapping-wing aircraft is established by an improved rigid finite element (IRFE) method. Second, a novel adaptive fault-tolerant controller based on the fuzzy neural network (FNN) and nonsingular fast terminal sliding-mode (NFTSM) control scheme are proposed for tracking control and vibration suppression of the flexible wings, while successfully addressing the issues of system uncertainties and actuator failures. Third, the stability of the closed-loop system is analyzed through Lyapunov's direct method. Finally, co-simulations through MapleSim and MATLAB/Simulink are carried out to verify the performance of the proposed controller.

Adaptive event-based robust passive fault tolerant control for nonlinear lateral stability of autonomous electric vehicles with asynchronous constraints

This work solves the robust passive fault-tolerant control problem for autonomous electric vehicles based on an adaptive event triggered mechanism. Firstly, given the system uncertainties from the tire dynamics and the longitudinal speed, the T-S fuzzy model method is used to approximate the vehicle lateral dynamics. Secondly, taking the communication constraints caused by band-limited networks into account, an adaptive event-triggered scheme is introduced in the process of the control design. Moreover, the asynchronous constraint of the weight function between the controller and system is considered. Thirdly, considering that the actuator faults are inevitably encountered in the control system, a robust passive fault-tolerant control method is proposed to improve vehicle performances. Finally, simulations are carried out to illustrate the effectiveness and robustness of the proposed approach.

Periodic Event-Triggered Integral Sliding-Mode Control for T-S Fuzzy Systems

This article investigates the integral sliding-mode control (SMC) problem for T-S fuzzy systems via the periodic event-triggered method. First, in order to remove the assumption that the inter-execution time has a uniform upper bound, a novel sliding variable error function is added into the event-triggering mechanism. Second, in order to avoid the extra information transmission, a new sliding-mode switching function consisting of the triggering state information is proposed to design the event-triggered integral SMC (ISMC) law. In addition, the ultimate boundedness of sliding motion can be ensured via using a designed event-triggered ISMC law. A sufficient condition of boundedness is given in the form of linear matrix inequality, which is employed to solve the controller gain matrix. Finally, the effectiveness of theoretical results can be illustrated via three illustrative examples.

Event-Triggered Security Consensus for Multi-Agent Systems with Markov Switching Topologies under DoS Attacks

This paper studies secure consensus control for multi-agent systems subject to denial-of-service (DoS) attacks. The DoS attacks cause changes in topologies, which will destroy the channels of communication and result in network paralysis. Unlike the existing publications with Markov switching, this paper mainly studies the topological structure changes of the subsystem models after DoS attacks. To ensure the consensus of systems, this paper designs an event triggered to reduce the use of the controller and decrease the influence of channel breaks off caused by DoS attacks. On this basis, different Lyapunov functions are established in each period of attack. Then, stochastic and Lyapunov stable theory is used to form the consensus criteria. Moreover, Zeno behavior is excluded by theoretical analysis. Finally, the simulation experiment proves the effectiveness of the proposed protocol.

Distributed Finite-Time Containment Control for Nonlinear Multiagent Systems With Mismatched Disturbances

This article proposes a finite-time adaptive containment control scheme for a class of uncertain nonlinear multiagent systems subject to mismatched disturbances and actuator failures. The dynamic surface control technique and adding a power integrator technique are modified to develop the distributed finite-time adaptive containment algorithm, which shows lower computational complexity. In order to overcome the difficulty from the mismatched uncertainties, the disturbance observers are constructed based on the backstepping technique. Moreover, the uncertain actuator faults, including loss of effectiveness model and lock-in-place model, are considered and compensated by the proposed adaptive control scheme in this article. According to the Lyapunov stability theory, it is demonstrated that the containment errors are practically finite-time stable in the presence of actuator faults. Finally, a simulation example is conducted to show the effectiveness of the proposed theoretical results.

Event-Based Robust Optimal Consensus Control for Nonlinear Multiagent System With Local Adaptive Dynamic Programming

This article investigates the robust optimal consensus for nonlinear multiagent systems (MASs) through the local adaptive dynamic programming (ADP) approach and the event-triggered control method. Due to the nonlinearities in dynamics, the first part defines a novel measurement error to construct a distributed integral sliding-mode controller, and the consensus errors can approximately converge to the origin in a fixed time. Then, a modified cost function with augmented control is proposed to deal with the unmatched disturbances for the event-based optimal consensus controller. Specifically, a single network local ADP structure with novel concurrent learning is presented to approximate the optimal consensus policies, which guarantees the robustness of the MASs and the uniform ultimate boundedness (UUB) of the neural network (NN) weights' estimation error and relaxes the requirement of initial admissible control. Finally, an illustrative simulation verifies the effectiveness of the method.

Cooperative Bipartite Containment Control for Multiagent Systems Based on Adaptive Distributed Observer

The cooperative bipartite containment control problem of linear multiagent systems is investigated based on the adaptive distributed observer in this article. The graph among the agents is structurally balanced. A novel distributed error term is designed to guarantee that some outputs of the followers converge to the convex hull spanned by the leaders, and the other followers' outputs converge to the symmetric convex hull. The matrices of the exosystems are not available for each follower. A general method is presented to verify the validity of a novel distributed adaptive observer rather than the previous approach. In other words, the definition of the M -matrix is not necessary in our result. Based on the distributed adaptive observer, an output-feedback control protocol is designed to solve the bipartite containment control problem. Finally, a numerical simulation is given to illustrate the effectiveness of the theoretical results.

Adaptive Neural Network Sliding Mode Control for a Class of SISO Nonlinear Systems

In this article, a sliding mode control (SMC) is proposed on the basis of an adaptive neural network (NN) for a class of Single-Input–Single-Output (SISO) nonlinear systems containing unknown dynamic functions. Since the control objective is to steer the system states to track the given reference signals, the SMC method is considered by employing the adaptive neural network (NN) strategy for dealing with the unknown dynamic problem. In order to compress the impaction coming from chattering phenomenon (which inherently exists in most SMC methods because of the discontinuous switching term), the boundary layer technique is considered. The basic design idea is to introduce a continuous proportional function to replace the discontinuous switching control term inside the boundary layer so that the chattering can be effectively alleviated. Finally, both Lyapunov theoretical analysis and computer numerical simulation are used to verify the effectiveness of the proposed SMC method.

Desired tracking of delayed quadrotor UAV under model uncertainty and wind disturbance using adaptive super-twisting terminal sliding mode control

In this study, the fully-actuated dynamic equation of quad-rotor as a type of Unmanned Aerial Vehicles (UAVs) is considered in the existence of input-delay, model uncertainty and wind disturbance. Then, a super-twisting terminal sliding mode control approach is planned with the aim of the finite-time attitude and position tracking of quad-rotor UAV considering input-delay, model uncertainty and wind disturbance. The finite time convergence of the tracking trajectory of quad-rotor is proved by Lyapunov theory concept. When the upper bound of the modeling uncertainty and wind disturbance is supposed to be unknown, an adaptive super-twisting terminal sliding mode control is proposed. Therefore, the unknown bounds of the model uncertainty and wind disturbance affecting the quad-rotor UAV are estimated using the adaptive-tuning control laws. Finally, simulation outcomes and experimental verifications are provided to demonstrate the validation and success of planned control technique.

Observer-based event-triggered type-2 fuzzy control for uncertain steer-by-wire systems

This paper addresses the tracking control problem for the uncertain steer-by-wire (SbW) system with the controller area network (CAN) communication and unavailable variables. First, an adaptive interval type-2 fuzzy logic system (IT2 FLS) and sliding mode observer are constructed to estimate the uncertain nonlinearity and unavailable variables of SbW control systems. Further, an event-triggered sliding mode control (ET-SMC) is presented to achieve the transient steering performance of SbW systems while saving CAN communication resources. Much importantly, the dynamic gain and nested technologies are incorporated in this scheme to deal with estimation error and the chattering phenomenon of the sliding mode control system. It is shown that the practical fixed-time stability of the closed-loop system can be guaranteed without the initial condition of tracking errors. Finally, simulations and vehicle experiments are presented to verify the designed scheme.

Adaptive Bipartite Tracking Control of Nonlinear Multiagent Systems With Input Quantization

This article studies the bipartite tracking control problem of distributed nonlinear multiagent systems with input quantization, external disturbances, and actuator faults. We use the radial basis function (RBF) neural networks (NNs) to model unknown nonlinearities. Due to the fact that the upper bounds of disturbances and the number of actuator faults are unknown, an intermediate control law is designed based on a backstepping strategy, where a compensation term is introduced to eliminate external disturbances and actuator faults. Meanwhile, a novel smooth function is incorporated into the real distributed controller to reduce the effect of quantization on the virtual controller. The proposed distributed controller not only realizes the bipartite tracking control but also ensures that all signals are bounded in the closed-loop systems and the outputs of all followers converge to a neighborhood of the leader output. Finally, simulation results demonstrate the effectiveness of the proposed control algorithm.

Event-Triggered Output-Feedback Control for Large-Scale Systems With Unknown Hysteresis

This article focuses on the event-triggered-based adaptive neural-network (NN) control problem for nonlinear large-scale systems (LSSs) in the presence of full-state constraints and unknown hysteresis. The characteristic of radial basis function NNs is utilized to construct a state observer and address the algebraic loop problem. To reduce the communication burden and the signal transmission frequency, the event-triggered mechanism and the encoding-decoding strategy are proposed with the help of a backstepping control technique. To encode and decode the event-triggering control signal, a one-bit signal transmission strategy is adopted to consume less communication bandwidth. Then, by estimating the unknown constants in the differential equation of unknown hysteresis, the effect caused by unknown backlash-like hysteresis is compensated for nonlinear LSSs. Moreover, the violation of full-state constraints is prevented based on the barrier Lyapunov functions and all signals of the closed-loop system are proven to be semiglobally ultimately uniformly bounded. Finally, two simulation examples are given to illustrate the effectiveness of the developed strategy.

Broadcast Event-Triggered Control Scheme for Multi-Agent Rendezvous Problem in a Mixed Communication Environment

This paper addresses the communication issue encountered by a hybrid controller when finding consensus in terms of the rendezvous target point in a broadcast and communication environment. This issue may result in a high level of computation and the utilization of agent resources when a continuous communication is required by agents to meet convergence requirements. Thus, an event-triggered system was integrated into the design of a broadcast and distributed consensus linear controller using the simultaneous perturbation stochastic algorithm (SPSA). The agent’s movement towards the rendezvous point is based on the broadcast value, whereas the next agent’s state position depends on the distributed local controller output. The communication error obtained during communication between the agent and neighbors is only added to the gradient approximation error of the SPSA if the event-triggered function is violated. As a result, in our model, the number of channel utilizations was lower and the agents’ performances were preserved. The efficiencies and effectiveness of the proposed controller have been compared with the traditional sampling broadcast time-triggered (BTT) approach. The time and iterations required by the broadcast event-triggered (BET) system were less than 40.42% and 21% on average as compared to BTT. The trajectory was not the same—the BET showed scattered movements at the initial stage, whereas BTT showed a linear movement. In terms of the number of channels, 28.91% of channels were preserved during the few hundred iterations. Consequently, a variety of hybrid controllers with event-triggered mechanisms can be proposed for other multi-agent motion coordination tasks.

Adaptive Fault-Tolerant Tracking Control for Discrete-Time Multiagent Systems via Reinforcement Learning Algorithm

This article investigates the adaptive fault-tolerant tracking control problem for a class of discrete-time multiagent systems via a reinforcement learning algorithm. The action neural networks (NNs) are used to approximate unknown and desired control input signals, and the critic NNs are employed to estimate the cost function in the design procedure. Furthermore, the direct adaptive optimal controllers are designed by combining the backstepping technique with the reinforcement learning algorithm. Comparing the existing reinforcement learning algorithm, the computational burden can be effectively reduced by using the method of less learning parameters. The adaptive auxiliary signals are established to compensate for the influence of the dead zones and actuator faults on the control performance. Based on the Lyapunov stability theory, it is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, some simulation results are presented to illustrate the effectiveness of the proposed approach.

Model-Free Optimized Tracking Control Heuristic

Many tracking control solutions proposed in the literature rely on various forms of tracking error signals at the expense of possibly overlooking other dynamic criteria, such as optimizing the control effort, overshoot, and settling time, for example. In this article, a model-free control architectural framework is presented to track reference signals while optimizing other criteria as per the designer’s preference. The control architecture is model-free in the sense that the plant’s dynamics do not have to be known in advance. To this end, we propose and compare four tracking control algorithms which synergistically integrate a few machine learning tools to compromise between tracking a reference signal and optimizing a user-defined dynamic cost function. This is accomplished via two orchestrated control loops, one for tracking and one for optimization. Two control algorithms are designed and compared for the tracking loop. The first is based on reinforcement learning while the second is based on nonlinear threshold accepting technique. The optimization control loop is implemented using an artificial neural network. Each controller is trained offline before being integrated in the aggregate control system. Simulation results of three scenarios with various complexities demonstrated the effectiveness of the proposed control schemes in forcing the tracking error to converge while minimizing a pre-defined system-wide objective function.