This article focuses on the private security of multiagent systems with external eavesdroppers. Note that the agent data/states finally reach the same value by using the consensus-based anti-eavesdroppers protocol with Laplace noises, which leads to the leakage possibility of the terminal information. To this end, a novel differential privacy protocol is designed based on directed signed networks, which yields the performance of$\xi$-differential privacy-preserving. To further reveal the effects of eavesdroppers on the system, the privacy disclosure proportion of groups (PDPGs) is proposed in the two cases of a single-channel eavesdropper and a multichannel eavesdropper. It is indicated that the PDPG of the resulting system does not exceed 50% even if the malicious adversary has the ability to crack the privacy-preserving mechanism. The effectiveness of the approach and its superiority over state-of-the-art counterparts are confirmed through numerical simulations.

This article deals with the optimal super-ellipse formation tracking control problem for multiple unmanned vehicles (MUVs), where each vehicle contains nonlinear uncertainties of unmodeled basic resistance, and the objective of energy optimization includes the super-ellipse orbit tracking energy and formation motion energy on the normal and tangent directions along the super-ellipse orbits, respectively. The communication topology is the directed leader-following structure. To avoid using the inputs of neighboring MUVs and the global communication information, a novel augmented formation input is designed and integrated into the formation motion subsystem. To deal with the uncertain nonlinearity, the uncertain virtual leader information, and the limited information of neighboring MUVs in the Hamilton-Jacobi–Bellman equations, a simplified reinforcement learning (RL) energy optimization method is designed based on identifier neural networks (NNs) and optimized backstepping technique. Theoretical stability analysis of system errors are given in detail. Simulation results show that the super-ellipse formation tracking energy consumption is significantly saved and the algorithm run time is decreased through comparison.

This paper proposes a novel Reverse Trajectory Prediction Enhanced Intent Recognition Algorithm (RTPEIR) that utilizes historical data to predict earlier trajectories and enhance intent recognition accuracy. The RTPEIR algorithm incorporates two main enhancements. Firstly, it leverages a combination of past and present trajectory data to reconstruct previous agent states, thereby providing a deeper understanding of agents' strategic developments. Secondly, it integrates these reconstructed trajectories with ongoing strategy recognition processes, significantly refining the predictive accuracy. Sim-ulation experiments conducted on the StarCraft Multi-Agent Challenge (SMAC) platform show that RTPEIR outperforms existing forward trajectory prediction models by 6.5%, and existing LSTM and GRU models by 13.3% and 14.4%, respectively, in terms of intent recognition accuracy. Furthermore, when combined with deep reinforcement learning algorithms, RTPEIR demonstrates a notable improvement in win rates, highlighting its effectiveness in complex multi-agent environments.

This article addresses the tracking control problem of nonlinear pure-feedback systems, where the control coefficients and the dynamics of the references are unknown. Fuzzy-logic systems (FLSs) are used to approximate the unknown control coefficients and at the same time the adaptive projection law is designed to allow each fuzzy approximation to cross zero, which yields that the proposed method avoids the assumption of using Nussbaum function, that is, the unknown control coefficients never cross zeros. Another adaptive law is designed to estimate the unknown reference and then it is intergraded into the saturated tracking control law to achieve the uniformly ultimately bounded (UUB) performance of the resulting closed-loop system. Simulations show the feasibility and effectiveness of the proposed scheme.

Spatiality and temporality represent key features of the real world. A critical hurdle in the application of fuzzy logic systems lies in their limited capability to directly approximate the variables across spatial and temporal scales. This article investigates the fuzzy approximation problem of uncertain nonlinear spatiotemporal systems. A novel multilayer fuzzy supremum approximation (MFSA) is designed to map a spatiotemporal function to a state-based iterative supremum function by separating the time-varying parameters, which can be further approximated using the proposed fuzzy upremum approximation algorithm. It is indicated that MFSA is an effective approximation method for spatiotemporal functions as compared to the references. Subsequently, MFSA is developed into the leader–following synchronization problem of discrete-time multiagent systems. The MFSA-based observer and synchronization control schemes are designed by removing the assumption that either the leader's control input or the bound of the leader's control input is a known prior to each follower. The uniformly ultimate boundedness of the observer estimation errors and synchronization errors are achieved. The corresponding simulations indicate the efficacy of our approach.

This brief addresses the neural network (NN) approximation problem for uncertain nonlinear systems with time-varying parameters (that is, unknown nonlinear spatiotemporal systems). Due to the fact that the unknown spatiotemporal functions cannot be directly approximated by NNs, a so-called time-varying parameter extraction is given to separate time-varying parameters from uncertain nonlinear spatiotemporal functions. By using the supremum of Euler norm of the extracted time-varying parameters, the nonlinear spatiotemporal function is mapped to an unknown state-based boundary function, which can be approximated by NNs. Based on the time-varying parameter extraction, an adaptive neural tracking control law is designed for uncertain strict-feedback nonlinear spatiotemporal systems, which guarantees the convergence of the tracking error with a trajectory performance. The effectiveness of the designed method is verified by simulations.

This article focuses on the average-tracking control issue for heterogeneous linear multiagent systems via a fixed-time approach. The agents, with varied dynamics and state dimensions, are subject to external disturbances and each has a unique reference signal that cannot be accessed by the other agents. In this setting, each agent is provided a multiple reference signal state compensator in order to estimate the states of all reference signals. Furthermore, external disturbances are estimated using a fixed-time sliding mode disturbance observer. An anti-disturbance control protocol is proposed by combining the disturbance observer and the state compensator for agents to track the average value of reference signals within a fixed time, which is predetermined and independent of initial states. The efficiency of the suggested average-tracking control mechanism is shown by numerical experiments.

This paper addresses the cooperative trajectory prediction problem of multiple UAVs in air combat. By using the historical trajectory information of each UAV and its neighbors, a novel GAN-CI algorithm is designed based on generate adversarial networks. The algorithm is used to generate multiple prediction trajectories through a generative adversarial network, and the input information is analyzed and processed by a cooperative information interaction module. It is shown that the algorithm improves the average prediction accuracy by 45% over the generative adversarial network without cooperative interaction information and 38% over the Long Short-Term Memory algorithm with pooling module.

The cooperation control of multiple intelligent agents (MIAs), which can solve complex engineering problems in practice, has received increasing attention. However, there are multiple disturbances in wireless sensor networks, which has a great effect on the collaboration of MIAs. In this paper, the problem of the flocking motion of second-order MIAs is addressed with collision avoidance and multiple disturbances. To estimate the matched/mismatched disturbances, the disturbance observers are designed. It is noted that the assumption that the differentials of disturbances converge to zeros in the literature is removed. A novel compound strategy is designed by using the robust auxiliary function and the potential function. The asymptotic properties of the flocking system are studied based on the Input-to-State Stability Theorem and the robust stability. Numerical simulation results verify the validity of the proposed protocol.

This paper presents applications of the continuous feedback method to achieve path-following and a formation moving along the desired orbits within a finite time. It is assumed that the topology for the virtual leader and followers is directed. An additional condition of the so-called barrier function is designed to make all agents move within a limited area. A novel continuous finite-time path-following control law is first designed based on the barrier function and backstepping. Then a novel continuous finite-time formation algorithm is designed by regarding the path-following errors as disturbances. The settling-time properties of the resulting system are studied in detail and simulations are presented to validate the proposed strategies.

This article addresses the spherical formation tracking control problem of nonlinear second-order vehicles moving in flowfields under both undirected networks and directed, strongly connected networks. Different from the previous adaptive estimate of the time-invariant parameters of flowfields, the flowfields under our consideration are spatial and absolutely unknown dynamics. Adaptive neural networks (ANNs) with the novel cooperative adaptive algorithms are proposed to approximate the flowfield acting on the channel of each vehicle's velocity (i.e., the mismatched flowfield) and the flowfield pushing the acceleration (i.e., the matched flowfield), respectively. For the purpose of avoiding the complex derivation derived from backstepping, the novel first-order filters are generated by dynamic surface based on barrier functions and relative positions of neighbors. The proposed control algorithms and adaptive upgrade law are fully distributed without using any global information of the graph. The uniform boundedness is analyzed in the Lyapunov sense. Simulation results are given to verify the theoretical analysis.

This article addresses the three-dimensional (3-D) coordinated control problem of directed networked aircraft-like vehicles, that is to track a set of given orbits on a sphere and achieve a lateral formation flight. Different from the case of Newton particles, a nonholonomic dynamics with unknown disturbances is considered. A novel method to decouple the spherical orbit tracking subsystem and the lateral formation flying subsystem is proposed. By overlooking the control of the vehicle’s surge velocity, a nonsmooth spherical orbit tracking algorithm is designed by backstepping. Without considering the spherical orbit tracking errors and using any global information of topologies, a distributed, nonsmooth formation protocol is designed. The input-to-state stability (ISS) theory is used to analyze the converge property of the interconnected system consisting of these two subsystems. Simulation results are given to verify the theoretical analysis.

This article addresses the containment control problem of multiagent systems under directed topologies, where the model of each agent is an unknown nonlinear nonaffine pure-feedback dynamic, and at the same time, the outputs and their derivatives of the leaders are unknown. To avoid the complex design process with the recursive methods (i.e., backstepping and dynamic surface), each unknown higher order nonlinear dynamic is transformed into a simple high-order integral model with unknown affine nonlinear terms in the last-order dynamic at first. Then, the fuzzy logic systems and the fuzzy state observers are constructed to approximate the unknown affine nonlinear terms and the unknown transformed states. Finally, a novel fully distributed fuzzy adaptive containment control law is generated according to the state observers and the supervised control. The stability of the closed-loop system is analyzed in the Lyapunov sense and the containment errors converge to a small neighborhood of the origin. Simulation results show the feasibility and effectiveness of the proposed scheme.

This paper takes the planar formation tracking control problem of second-order agents with model uncertainties into consideration. A novel adaptive neural network (ANN) estimation method based on neighborhood information is designed to estimate model uncertainties. By using the tools of the back-stepping method and ANN, a robust formation tracking control law is given. The law can guarantee this formation tracking errors uniformly bounded under connected topologies. Numerical simulation results verify the validity of the analysis results.

In this article, an indirect adaptive fuzzy control scheme is proposed for single-input, single-output (SISO) nonaffine nonlinear systems in a pure-feedback form. In this scheme, the unknown nonlinear functions are approximated by Takagi-Sugeno (T-S) fuzzy logic systems with an state observer. The adaptive laws are developed to adjust the parameters of the fuzzy systems. The stability of the closed-loop system is proved with all state variables being uniformly bounded in the Lyapunov sense and the tracking error is confirmed to zero asymptotically. Finally, simulation results obtained for two practical examples show the feasibility and effectiveness of the proposed scheme.

This paper addresses the robust cooperative control for lateral formation tracking a set of circles on the given sphere in an absolutely unknown spatial flowfield. Different from the adaptive estimation method for the unknown flow speed with knowledge of the velocity direction in the literatures, a novel adaptive neural estimate is constructed based on the neighbors' information to approximate the unknown flow velocity. It is noted that such neighbor-based adaptive neural estimation develops the traditional adaptive neural approach by consensus. Then, a robust spherical formation tracking control law is established according to flow estimation. The uniform ultimate boundedness is proven when the communication topology associated with networked first-order agents. The effectiveness of the analytical results is verified by numerical simulations.

This paper considers the cooperative control problem of second-order agents formation tracking a set of given curves on spheres when each agent suffers an unknown spatiotem-poral flowfield. The flowfield under consideration is composed of three known base vectors and the unknown corresponding coefficients. A novel coordinated adaptive estimator is proposed to estimate the unknown flow coefficients based on the neighbor to neighbor information. Adaptive backstepping, the geometric extension design and consensus are combined to design the robust spherical formation tracking control law. The effectiveness of the analytical results is verified by numerical simulations.

This paper considers the problem of directing a family of underactuated ships to formation tracking a set of closed orbits and achieve attitude synchronization. It shows that our previous concentric compression design is useful to the coordinated motion of underactuated ships. The condition that the total linear speed of each ship is greater than zero is ensured by introducing a potential function. Asymptotical stabilization is proved when the inter-ship communication topology is bidirectional. The theoretical result is proved by a numerical example.