Abstract: This paper considers the human-in-the-Ioop leader-following consensus control problem of multi-agent systems (MASs) with unknown matched nonlinear functions and actuator faults. It is assumed that a human operator controls the MASs via sending the command signal to a non-autonomous leader which generates the desired trajectory. Moreover, the leader's input is nonzero and not available to all followers. By using neural networks and fault estimators to approximate unknown nonlinear dynamics and identify the actuator faults, respectively, the neighborhood observer-based neural fault-tolerant controller with dynamic coupling gains is designed. It is proved that the state of each follower can synchronize with the leader's state under a directed graph and all signals in the closed-loop system are guaranteed to be cooperatively uniformly ultimately bounded. Finally, simulation results are presented for verifying the effectiveness of the proposed control method.

Abstract: In this article, an adaptive optimized formation control problem is studied for the second-order stochastic multiagent systems (MASs) with unknown nonlinear dynamics. Compared with first-order formation control, the second-order MASs consider not only the states but also the states rates, which is certainly more challenging and difficult work. In the control design of this article, the fuzzy logic systems are applied to approximate the nonlinear functions. By employing the actor-critic architecture and Lyapunov stability theory, the proposed optimal formation control strategy ensures that all the error signals are bounded in probability. Finally, the simulation examples verify that the proposed formation control approach achieves desired results.

Abstract: 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.

Abstract: This article focuses on scaled consensus tracking for a class of high-order nonlinear multiagent systems Different from the existing results, for high-order nonlinear multiagent systems with time delays and external disturbances, a fully distributed consensus protocol is designed to drive all agents to achieve scaled consensus with preassigned ratios The control gains are varying and updated by distributed adaptive laws As a result, the presented protocol is independent of any global information, and thus, could be implemented in a fully distributed manner Simultaneously, the fully distributed control protocol using an adaptive $\sigma$ -modification technique is presented to deal with external disturbances, which can guarantee the tracking errors and coupling weights of all following agents are uniformly ultimately bounded To tackle with the derivatives of the functionals with time delays, the Lyapunov–Krasovskii functional is employed to analyze and compensate them by introducing multiintegral terms Finally, simulation examples are included to verify the effectiveness of the theoretical results

Abstract: This article investigates the adaptive neural network fixed-time tracking control issue for a class of strict-feedback nonlinear systems with prescribed performance demands, in which the radial basis function neural networks (RBFNNs) are utilized to approximate the unknown items. First, an modified fractional-order command filtered backstepping (FOCFB) control technique is incorporated to address the issue of the iterative derivation and remove the impact of filtering errors, where a fractional-order filter is adopted to improve the filter performance. Furthermore, an event-driven-based fixed-time adaptive controller is constructed to reduce the communication burden while excluding the Zeno-behavior. Stability results prove that the designed controller not only guarantees all the signals of the closed-loop system (CLS) are practically fixed-time bounded, but also the tracking error can be regulated to the predefined boundary. Finally, the feasibility and superiority of the proposed control algorithm are verified by two simulation examples.

Abstract: In this brief, an adaptive fuzzy tracking control method is proposed for switched multi-input multi-output (MIMO) nonlinear systems with time-varying full state constrains (TFSCs) and unknown control directions. First, the fuzzy logic systems are utilized to approximate unknown dynamic functions. A tangent barrier Lyapunov function (BLF-Tan) is used to solve the problem of TFSCs, and the unknown control directions problem is addressed by applying Nussbaum-type function. Then, an adaptive tracking controller is constructed by the backstepping technique. Under the designed control scheme, all the systems signals are derived to be bounded, and the tracking error of the systems is converged to a neighborhood near zero. Finally, the simulation example illustrates the control design programme is reasonable and effective.

Abstract: This article studies the hierarchical sliding-mode surface (HSMS)-based adaptive optimal control problem for a class of switched continuous-time (CT) nonlinear systems with unknown perturbation under an actor–critic (AC) neural networks (NNs) architecture. First, a novel perturbation observer with a nested parameter adaptive law is designed to estimate the unknown perturbation. Then, by constructing an especial cost function related to HSMS, the original control issue is further converted into the problem of finding a series of optimal control policies. The solution to the HJB equation is identified by the HSMS-based AC NNs, where the actor and critic updating laws are developed to implement the reinforcement learning (RL) strategy simultaneously. The critic update law is designed via the gradient descent approach and the principle of standardization, such that the persistence of excitation (PE) condition is no longer needed. Based on the Lyapunov stability theory, all the signals of the closed-loop switched nonlinear systems are strictly proved to be bounded in the sense of uniformly ultimate boundedness (UUB). Finally, the simulation results are presented to verify the validity of the proposed adaptive optimal control scheme.

Abstract: This article is concerned with the ultimately bounded filtering problem for a class of linear time-delay systems subject to norm-bounded disturbances and impulsive measurement outliers (IMOs). The considered IMOs are modeled by a sequence of impulsive signals with certain known minimum norm (i.e., the minimum of the norms of all impulsive signals). In order to characterize the occasional occurrence of IMOs, a sequence of independent and identically distributed random variables is introduced to depict the interval lengths (i.e., the durations between two adjacent IMOs) of the outliers. In order to achieve satisfactory filtering performance, a novel parameter-dependent filtering approach is proposed to protect the filtering performance from IMOs by using a special outlier detection scheme, which is developed based on a particular input–output model. First, the ultimate boundedness (in mean square) of the filtering error is investigated by using the stochastic analysis technique and the Lyapunov-functional-like method. Then, the desired filter gain matrix is derived through solving a constrained optimization problem. Furthermore, the designed filtering scheme is applied to the case where the statistical properties about the interval lengths of outliers are completely unknown. Finally, a simulation example is provided to demonstrate the effectiveness of our proposed filtering strategy.

Abstract: An event-triggered adaptive dynamic programming (ADP) algorithm is developed in this article to solve the tracking control problem for partially unknown constrained uncertain systems. First, an augmented system is constructed, and the solution of the optimal tracking control problem of the uncertain system is transformed into an optimal regulation of the nominal augmented system with a discounted value function. The integral reinforcement learning is employed to avoid the requirement of augmented drift dynamics. Second, the event-triggered ADP is adopted for its implementation, where the learning of neural network weights not only relaxes the initial admissible control but also executes only when the predefined execution rule is violated. Third, the tracking error and the weight estimation error prove to be uniformly ultimately bounded, and the existence of a lower bound for the interexecution times is analyzed. Finally, simulation results demonstrate the effectiveness of the present event-triggered ADP method.

Abstract: An adaptive decentralized asymptotic tracking control scheme is developed in this paper for a class of large-scale nonlinear systems with unknown strong interconnections, unknown time-varying parameters, and disturbances. First, by employing the intrinsic properties of Gaussian functions for the interconnection terms for the first time, all extra signals in the framework of decentralized control are filtered out, thereby removing all additional assumptions imposed on the interconnections, such as upper bounding functions and matching conditions. Second, by introducing two integral bounded functions, asymptotic tracking control is realized. Moreover, the nonlinear filters with the compensation terms are introduced to circumvent the issue of “explosion of complexity”. It is shown that all the closed-loop signals are bounded and the tracking errors converge to zero asymptotically. In the end, a simulation example is carried out to demonstrate the effectiveness of the proposed approach.

Abstract: In this article, we investigate the periodic event-triggered synchronization of discrete-time complex dynamical networks (CDNs). First, a discrete-time version of periodic event-triggered mechanism (ETM) is proposed, under which the sensors sample the signals in a periodic manner. But whether the sampling signals are transmitted to controllers or not is determined by a predefined periodic ETM. Compared with the common ETMs in the field of discrete-time systems, the proposed method avoids monitoring the measurements point-to-point and enlarges the lower bound of the inter-event intervals. As a result, it is beneficial to save both the energy and communication resources. Second, the “discontinuous” Lyapunov functionals are constructed to deal with the sawtooth constraint of sampling signals. The functionals can be viewed as the discrete-time extension for those discontinuous ones in continuous-time fields. Third, sufficient conditions for the ultimately bounded synchronization are derived for the discrete-time CDNs with or without considering communication delays, respectively. A calculation method for simultaneously designing the triggering parameter and control gains is developed such that the estimation of error level is accurate as much as possible. Finally, the simulation examples are presented to show the effectiveness and improvements of the proposed method.

Abstract: This article investigates the problem of fuzzy adaptive consensus tracking control for nonlinear multiagent systems with unknown nonlinear control gain functions. In the control design, fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics, and a distributed state observer is constructed to estimate the unmeasured states. Under the case of directed graph, by constructing the logarithm Lyapunov functions, an adaptive fuzzy distributed control method is presented, which removes the restrictive assumptions about the unknown control gain functions must be constants in traditional adaptive intelligent output feedback control methods. The developed control scheme cannot only ensure that all signals of the controlled system are semiglobal uniformly ultimately bounded, but also make the outputs of all the followers keep consensus with the output trajectory of the leader. Finally, simulation results are given to illustrate the effectiveness of the developed consensus control scheme and theorem.

Abstract: The distributed tracking problem for uncertain nonlinear multiagent systems (MASs) under event-triggered communication is an important issue. However, existing results provide solutions that can only ensure stability with bounded tracking errors, as asymptotic tracking is difficult to be achieved mainly due to the errors caused by event-triggering mechanisms and system uncertainties. In this article, with the aim of overcoming such difficulty, we propose a new methodology. The subsystems in MASs are divided into two groups, in which the first group consists of the subsystems that can access partial output of the reference system and the second one contains all the remaining subsystems. To estimate the state of the reference system, a new distributed event-triggered observer is first designed for the first group based on a combined output observable condition. Then, a distributed event-triggered observer is proposed for the second group by employing the observer state of the first group. Based on the designed observers, adaptive controllers are derived for all subsystems. It is established that global stability of the closed loop system is ensured and asymptotic convergence of all the tracking errors is achieved. Moreover, a simulation example is provided to show the effectiveness of the proposed method.

Abstract: This brief investigates the reachable set estimation problem of the delayed Markovian jump neural networks (NNs) with bounded disturbances. First, an improved reciprocally convex inequality is proposed, which contains some existing ones as its special cases. Second, an augmented Lyapunov-Krasovskii functional (LKF) tailored for delayed Markovian jump NNs is proposed. Thirdly, based on the proposed reciprocally convex inequality and the augmented LKF, an accurate ellipsoidal description of the reachable set for delayed Markovian jump NNs is obtained. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

Abstract: This letter investigates the recursive state estimation (RSE) problem for a class of coupled output complex networks via the dynamic event-triggered communication mechanism (DETCM) and innovation constraints (ICs). Firstly, a DETCM is employed to regulate the transmission sequences. Then, in order to improve the reliability of network communication, a saturation function is introduced to constrain the measurement outliers. A new RSE method is provided such that, for all output coupling, DETCM and ICs, an upper bound of state estimation error covariance (SEEC) is presented in a recursive form, whose trace can be minimized via parameterizing the state estimator gain matrix (SEGM). Moreover, the theoretical analysis is given to guarantee that the error dynamic is uniformly bounded. Finally, a simulation example is illustrated to show the effectiveness of the proposed RSE method.

Abstract: This article investigates the neural-network-based adaptive predefined-time tracking control problem for switched nonlinear systems. Neural networks are employed to approximate the unknown part of nonlinear functions. The finite-time differentiators are introduced to estimate the first derivative of the virtual controllers. Then, a novel adaptive predefined-time controller is proposed by utilizing the backstepping control technique and the common Lyapunov function (CLF) method. It is explained by the theoretical analysis that the developed controller guarantees that all signals of the switched closed-loop systems are bounded under arbitrary switchings and the tracking error converges to zero within the predefined time. A simulation is shown to verify the validity of the developed predefined-time control approach.

Abstract: Exponential Euler discrete schemes have been widely employed in the studies of Caputo fractional order differential equations, but almost no literature concerns the Caputo–Fabrizio case. In current work, exponential discrete form has been set up to study Caputo–Fabrizio fuzzy BAM neural networks (CF-FBAMNNs). The research findings tell someone that (1) the exponential discrete form characterizes the continuous CF-FBAMNNs superior to the classical Euler discrete technique; (2) this type discrete technique pertains to the implicit Euler form, which can be calculated by PECE algorithm. Furthermore, the existence of a unique bounded asymptotically almost automorphic sequence solution and global exponential stability of the proposed discrete-time models are investigated. More importantly, the current works make up for the lacks in the existing literatures and build a set of new theories and methods in studying discrete-time Caputo–Fabrizio models in the fields of science and engineering.

Abstract: Studying the dynamics of several nonlinear structures that arise in nonlinear science including optical fiber and various plasma models in a nonplanar (cylindrical and spherical) geometry is closer to reality rather than the one-dimensional planar geometry. Motivated by this point and based on the laboratory results and satellite observations, thus, this work is performed to derive some novel general analytical approximations (including any nonplanar modulated structures like rogue waves (RWs), breathers, bright and dark envelope solitons, etc.) to a nonplanar nonlinear Schrödinger equation (nNLSE) using the ansatz method. Based on this method, two general formulas for the analytical approximations are derived. The most important characteristic of the obtained approximations is that they are general solutions that can be employed for studying any modulated nonplanar structures described by the nNLSE. The residual error formulas for the cylindrical and spherical rational solutions are derived and discussed numerically to verify the precision of the obtained approximations. Also, the nNLSE is analyzed numerically via the method of lines (MOLs). Moreover, a comparison between analytical and numerical approximations is carried out. As a real application to the obtained solutions, the propagation of nonplanar rational solutions including rogue waves (RWs) and breathers structures in a dusty plasma are investigated. The obtained approximations will quickly find acceptance in dealing with the bounded nonlinear phenomena in different plasma models and many other branches of science.

Abstract: This article discusses the prescribed performance control problem for multiagent systems involving the state triggering and the controller output triggering simultaneously. To successfully apply the backstepping technique in the event-triggered control design, the virtual control signal is constructed by the original system state. Compared with the existing results on the prescribed performance, a new barrier Lyapunov function is developed with considering the characteristics of multiagent systems, and a fuzzy adaptive event-triggered control protocol is proposed by the backstepping procedure. It guarantees that the consensus tracking error converges to a predefined region of the origin in a preset finite time. At the same time, all other closed-loop signals remain bounded without the Zeno behavior. Finally, a simulation example confirms the availability of the developed control scheme with a comparison.

Abstract: This article solves the problem of proximate fixed-time prescribed performance trajectory tracking for robot manipulators in the presence of bounded external disturbances and parametric uncertainties. A novel prescribed performance function (PPF) is first presented. A sliding surface with the prescribed performance tracking errors is constructed and a nonsingular proximate fixed-time terminal sliding mode prescribed performance control (FTSMPPC) is developed. It is proved that the position tracking error satisfies the prescribed performance boundaries all the time and globally converges to a preset small region centered on the origin within fixed time and then converges to the origin asymptotically. The proposed FTSMPPC provides faster transient performance quantified and higher steady-state accuracy by the proposed PPF. The effectiveness and improved performances of the presented approach are validated by simulations and experiments.