The issue related to distributed containment control for multiple networked mechanical systems with inherent nonlinearities, dynamic leaders, unknown external disturbances, parameter uncertainties, and constrained network communication is investigated by designing distributed adaptive event-triggered sliding-mode controllers in this study. To lessen the number of state updates and network resource loss of networked mechanical systems, a time-varying-threshold-based adaptive event-triggered mechanism is constructed. An adaptive sliding-mode estimator is established to estimate the inaccurate states. Then, integrated with the aforementioned event-triggered strategy and adaptive sliding-mode estimator, discontinuous and continuous distributed adaptive event-triggered sliding-mode control laws without requiring each follower to get the upper bounds of the leaders’ states derivatives are, respectively, devised to compensate for the influences of nonlinearities, disturbances, and parameter uncertainties. To further attenuate the negative effects of unknown disturbances, inherent nonlinearities, and chattering, a distributed adaptive event-triggered sliding-mode control protocol with boundary layer function is designed. Eventually, the Lyapunov stability theory is utilized to testify that the adaptive error and containment error are uniformly ultimately bounded. A practical example is furnished to verify the validity of the present sliding-mode containment control strategies.Note to Practitioners—This work aims to develop the distributed containment control approach for multiple networked nonlinear mechanical systems, which is of great significance in the fields of deep space exploration, environment monitoring and joint rescue. We put forward an event-based adaptive estimation and containment control framework for multiple networked nonlinear mechanical systems, which solves practical problems such as transmission frequency, limited computation capability, and network resources. An adaptive sliding-mode estimator and adaptive event-triggered mechanism are, respectively, devised to estimate the inaccurate states and reduce data transmission frequency. Despite the effects of communication interruption and unknown disturbances, an event-triggered adaptive control protocol based on sliding-mode estimator is designed, which is applied to a planar manipulator with two degree-of-freedom.

This article focuses on the issue of the quantization-based event-triggered integral sliding-mode controller design for networked multiagent systems (MASs) encountering interferences under limited network bandwidth. An integral sliding manifold (ISM) is designed to address the effect of disturbances and ensure the desired dynamic performance of the system. We establish an event-triggered mechanism (ETM) with an exponential decay rate to conserve the limited communication resources. Then, a uniform quantizer is added to quantify the triggered state signals to lessen the network transmission burden caused by the digital network. Combining the designed ETM with a static uniform quantizer, the quantized trigger state signals are sent to decoders through the digital network to construct a quantized ISM. Subsequently, an event-triggered integral sliding-mode controller under quantization technology is developed to ensure the asymptotic average consensus of networked MASs. By testifying that every network agent has a lower positive bound, the viability of the proposed ETM is demonstrated, thereby ensuring the absence of Zeno behavior. Eventually, two simulation examples are proffered to confirm the efficacy of the quantization feedback-based event-triggered sliding-mode control methodology.

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.

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.

The bounded antisynchronization (AS) problem of multiple discrete-time neural networks (NNs) based on the fuzzy model is studied, in consideration of the differences in quantity and communication among different NN groups, the variabilities of dynamics, and communication topological affected by environments. To reduce the energy consumption of communication, a cluster pinning communication mechanism is proposed, and an impulsive observer is designed to estimate the state of target NN. Then, a multilevel hybrid controller based on the impulsive observer is built including the AS controller and the bounded synchronization (BS) controller. Sufficient conditions for bounded AS are obtained by analyzing the stability of the BS augmented error (BSAE) and the AS augmented error (ASAE) based on the fuzzy-based Lyapunov functional (FBLF). Finally, a numerical example and an application example are given to verify the validity of the obtained results.

This article focuses on the distributed adaptive fixed-time platoon tracking problem for third-order fully heterogeneous nonlinear vehicles. The modified dynamics of each vehicle are constructed, and a practically fixed-time criterion is set up. Moreover, the singularity problem in the fixed-time and finite-time control is addressed well by designing new virtual signals and exploiting the inequality technique and power transformation scheme instead of the approximation method. The distributed nonlinear fixed-time tracking protocol is constructed by virtue of the recursive algorithm, and the design process is simplified by a tracking differentiator. In particular, the upper bound of the settling time has nothing to do with initial conditions. Further, the disturbances are tackled via robust$H_{\infty }$control theory. Finally, simulation tests are contained to illustrate the performance of the proposed protocols.

This article investigates the adaptive consensus control problem for a group of multirotor unmanned aerial vehicles (MUAVs) subject to dynamic state constraints and unmatched external disturbances. An adaptive inner–outer loop controller is devised based on the backstepping method, where the issue of “explosion of complexity” is solved via a first-order sliding-mode differentiator. By introducing a barrier function-based state transformation technique into the outer loop controller design, the dynamic constraints covering different types of time-varying state constraints can be addressed without reconfiguring the controller structure. Meanwhile, a neural-network-based disturbance observer is constructed to estimate the external disturbances. Consequently, the applicability and robustness of controller are improved, such that the position tracking control can be implemented in severe environments. Moreover, the inner loop controller is established by virtue of a distributed sliding-mode estimator so as the consensus control for attitude systems of multiple MUAVs can be realized rapidly. Finally, a simulation example is presented to demonstrate the validity and superiority of the proposed control strategy.

This paper investigates the secure consensus tracking problem for continuous-time nonlinear multiagent systems with sensor attacks. By designing a secure data selector, the unattacked output data is extracted from a group of output measurements under sparse sensor attacks. Then, by virtue of the obtained data and neural networks, a state observer is constructed to estimate the unavailable system states, where the convex combination theory is introduced to reduce the difficulty of solving observation gains. To utilize the limited communication resources reasonably, a novel saturated threshold event-triggered control strategy is proposed to reduce control updates, and then each update is encoded into a binary signal (0 or 1) to further reduce the occupation of communication bandwidth. The designed control scheme ensures that all closed-loop signals are semi-globally uniformly ultimately bounded, and its effectiveness is verified via a simulation of attitude control of unmanned aerial vehicles.

This article focuses on the distributed cooperative compound tracking issue of the vehicular platoon. First, a definition, called compound tracking control, is proposed, which means that the practical finite-time stability and asymptotical convergence can be simultaneously satisfied. Then, a modified performance function, named finite-time performance function, is designed, which possesses the faster convergence rate compared to the existing ones. Moreover, the adaptive neural network (NN), prescribed performance technique, and backstepping method are utilized to design a distributed cooperative regulation protocol. It is worth noting that the convergence time of the proposed algorithm does not depend on the initial values and design parameters. Finally, simulation experiments are given to further verify the effectiveness of the presented theoretical findings.

The problem of secure finite-horizon consensus control for discrete time-varying multiagent systems (MASs) with actuator saturation and cyber attacks is addressed in this article. A random attack model is first proposed to account for randomly occurring false data injection attacks and denial-of-service attacks, whose dynamics are governed by the random Markov process. The hybrid secure control scheme is developed to mitigate the influence of arbitrary cyber attacks on system performance. Specifically, this article proposes a hybrid control law containing multiple controllers, each of which is designed to counter different types of cyber attacks. By using the stochastic analysis approach, two sufficient criteria are provided to guarantee that the time-varying MASs satisfy the finite horizon$H_{\infty }$consensus performance. Then, the controller parameters are obtained by solving the recursive linear matrix inequality. The usefulness of the theoretic results presented is demonstrated via a numerical example that contains a performance comparison of different secure control schemes.

This article deals with the event-triggered leader-following guaranteed cost consensus control problem for second-order nonlinear multiagent systems, in which the guaranteed cost function is proposed to facilitate to enhance the consensus tracking regulation performance. To reduce the frequency of information transmission, a distributed event-triggered mechanism, which broadcasts the triggered states to its neighbours for each agent, is designed, and the triggering condition is then constructed for leader-following second-order nonlinear multiagent systems. By employing Lyapunov–Krasovskii method and Barbalat’s lemma, some sufficient conditions are derived to ensure the leader-following consensus and guaranteed cost performance for second-order nonlinear multiagent systems. It is also exhibited that the constructed triggering condition can efficaciously exclude the Zeno behavior. To testify the efficacy of the proposed theoretical methodology, a simulation example is offered.

The problem of leader-following consensus fault-tolerant control is investigated for multiagent systems (MASs) with time-varying nonaffine nonlinear faults, where the interactive topology is directional. In this article, to guarantee the performance consensus on tracking error, in the design process, the inherent problem of “explosion of complexity” is solved by the dynamic surface control technique. Fuzzy logic systems are employed to approximate the unknown nonlinearity effects and changes in model dynamics due to faults. A fuzzy state observer is presented to estimate the unmeasured states. According to the backstepping technique, a distributed consensus fuzzy controller is developed to guarantee that output signals of all followers and leader are synchronized. It can be proved that all variables of MASs are uniformly ultimately bounded. Finally, the validity of the control scheme is illustrated by some simulation results.

This article investigates the problem of adaptive neural sliding mode control for Markov jump systems. The transition probabilities of the Markov process are partly unknown. The cyber layer, which is vulnerable to the adversary, is deployed to broadcast the control signal to the actuator. The attacker can inject malicious information to the control signal to deteriorate the system performance. A sliding mode controller is designed to stabilize the system. Then, sufficient conditions that ensure the stability of the closed-loop system are given in the framework of the Lyapunov theory. In the end, two simulation examples are applied to illustrate the effectiveness and feasibility of the proposed methodology.

The event-triggered tracking control problem of second-order multiagent systems in consideration of system nonlinearities is investigated by utilizing the distributed sliding-mode control (SMC) approach. An event-triggered strategy is proposed to decrease the controller sampling frequency and save the network communication resources; the triggering condition is then established for leader-following multiagent systems. In this article, by utilizing the distributed event-based sliding-mode controller, the system state of second-order multiagent systems with system nonlinearities is capable of approaching the integral sliding-mode surface in finite time. A novel integral sliding-mode surface is constructed in this article to guarantee the consensus tracking performance in the existence of system nonlinearities as the state trajectories of second-order integrator systems move on the constructed sliding manifold. By employing the Lyapunov approach, sufficient conditions are deduced to ensure that the consensus tracking performance is obtained for the closed-loop system. Furthermore, it is presented that the triggering scheme can effectively reduce state updates and eliminate the Zeno behavior. A simulation example is provided to testify the validity of our proposed methodology.

This paper studies the problem of event-triggered sliding mode control of discrete-time Markov jump systems (MJSs). Two kinds of classical control schemes, which are observer-based control and state-feedback control schemes, are employed to handle the proposed synthesis problem. The event-triggered observer-based sliding mode controller and event-triggered state-feedback sliding mode controller are established by plunge of discrete-time event detectors into the studied control system, respectively. Moreover, the proposed event-triggered sliding mode controllers can guarantee the MJSs to be stochastically stable with H∞performance, and ensure the finite-time reachability of the specified sliding manifold. Simulation results are provided to illustrate the effectiveness of the proposed theoretical results.

This paper studies the state estimator design for periodic neural networks, where stochastic weight matrices B(k) and packet dropouts are considered. The stochastic variables, which may influence each other, are introduced to describe uncertainties of weight matrices. In order to model the time-varying conditions of the communication channel, a Markov chain is employed to study the jumping cases of the stochastic properties of the packet dropouts (i.e., Bernoulli process with jumping means and variances being used to handle the packet dropouts). A state estimator is constructed such that the augmented system is stochastically stable and satisfies the H∞performance. The estimator parameters are derived by means of the linear matrix inequalities method. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.