This paper studies the distributed tracking for the nonlinear multi-agent systems perturbed by second-order moment processes. What makes the case here unique from the prior results is that on the one hand, the system is more practical than those with white noise since it is more in line with practical engineering applications, and on the other hand, the system has inherently nonlinear distinguishing from those with second-order moment processes. In this paper, a distributed tracking controller is designed by employing the algebraic graph theorem and the distributed backstepping method, in which, extensive computational skills are taken to offset the difficulties from the system’s high-order. Furthermore, by using stochastic control theory, the tracking errors can be adjusted to an arbitrarily small value while all the states of the closed-loop system composed by the multi-agent systems are bounded in probability. At last, a simulation example with three agents demonstrates the effectiveness of the distributed tracking controller.

The paper investigates the bipartite synchronization problem of memristive coopetition neural networks under the DoS attacks, which is based on a Zeno-free resilient event-triggered control scheme. The reasons for considering this problem are mainly the following two: (1) Considering the effects of memristive weights and competitive interactions while defending against DoS attacks has both theoretical significance and practical implications. (2) Designing a corresponding controller and Lyapunov function to obtain a secure synchronization criterion is challenging. Based on these two reasons, coordinate transformation techniques and interval matrix methods are used to address competitive interactions and memristive weights, respectively. Furthermore, an error system model is established. Then, a novel resilient sampling scheme is proposed, integrating the Zeno-free event-triggered mechanism with the characteristics of the attacks. Taking into account the resilient sampling scheme, memristive residuals, and competitive interactions, a pinning Zeno-free resilient event-triggered controller is constructed. Further, utilizing information from periodic sampling, triggering intervals within the triggering mechanism, and DoS attack intervals, a positive definite and continuous interval-dependent Lyapunov function is constructed. By combining stability theory, inequality techniques, and convex combination methods, a bipartite secure synchronization criterion is obtained. Finally, the simulation results verify the effectiveness and advantages of the Zeno-free resilient event-triggered control strategy in addressing this problem.

This paper focuses on the predefined-time cooperative trajectory tracking control for unmanned surface vessels (USVs) within a leader-follower framework with unknown velocity of the leader USV. Firstly, a novel virtual USV is designed which for the first time estimates the velocity of the leader USV within a predefined time. Secondly, by integrating the virtual USV system and backstepping technology, a predefined-time virtual control law and an actual control law are proposed, enabling the leader USV and the follower USV to navigate synchronously within a predefined time. The designed controller guarantees that all error signals of the overall closed-loop tracking system are practically predefined-time stable and converges to a small neighborhood around the origin. Simulation and experimental results validate the correctness and effectiveness of the proposed method.

In this paper, the problem of prescribed-time tracking control with unified prescribed performance is studied for multi-input multi-output (MIMO) nonlinear systems with mismatched nonvanishing disturbances, actuator faults, and time-varying control coefficients whose sign and magnitude are both unknown. On the one hand, a novel prescribed-time stability criterion using Nussbaum functions is proposed to deal with the issues raised by the presence of mismatched nonvanishing disturbances, actuator faults, and time-varying control coefficients. This criterion is of independent interest and can be used beyond the control problem addressed in this paper. On the other hand, based on the proposed stability criterion, a prescribed-time tracking control framework is developed so that the tracking error converges to zero within a prescribed time, in the presence of the aforementioned complicating factors. Compared with existing asymptotic stability results for uncertain MIMO nonlinear systems subject to unknown control coefficients, the proposed framework guarantees that the tracking error remains within the unified prescribed performance boundary, which is uniform with respect to different initial tracking errors, thereby eliminating the need for controller redesign and stability reanalysis. The proposed control method is verified via an electromechanical system and a robot manipulator system in numerical simulation.

In this paper, a finite-time trajectory tracking control strategy is proposed for unmanned surface vehicles (USVs) with composite disturbances. First, to address the chattering phenomenon from unknown disturbances, a hysteretic quantizer is introduced, which filters out minor fluctuations in the input signal. Second, a finite-time disturbance observer is proposed to precisely estimate the composite disturbances, which combine model uncertainty and unknown time-varying external disturbances. Then, a finite-time command filter is employed to derive the virtual control law while avoiding singularity issues, followed by the design of a backstepping-based controller. By using the stability theory, it is proved that the closed-loop system is finite-time stable. Finally, the simulation results verify the effectiveness of the proposed control strategy.

In this paper, the problem of mean-square bipartite synchronization of coopetition neural networks under deception attacks is considered. Firstly, the zero-row-sum Laplacian matrix is derived via coordinate transfor mation methods. Based on the characteristics of deception attacks, an appropriate pinning sampled-data control strategy is designed, thereby deriving the error system model. Next, a nonpositive-definite discontinuous interval-dependent looped-function is constructed, and based on this, a new lemma regarding mean-square bipartite synchronization is proposed. Subsequently, by combining discrete Lyapunov theory and inequality techniques, a linear matrix inequality-based criterion for mean square bipartite synchronization is derived. Finally, a numer ical example is provided to validate the effectiveness and advantages of the constructed Lyapunov function in reducing the minimum allowable coupling strength, increasing the maximum allowable sampling interval, and enhancing the maximum allowable deception attack rate.

We propose a globally smooth time-varying dynamic gain scheduled control scheme for chained nonholonomic systems with linear and bilinear chained subsystems. Key properties of parametric Lyapunov equations are exploited to design an exponentially convergent controller for the linear subsystem. Subsequently, a linear time-varying state transformation converts the bilinear subsystem into a time-varying system, based on which smooth dynamic gain scheduled controllers are constructed. In contrast to traditional static gain-scheduled methods for non-holonomic systems, which only consider kinematic nonholonomic systems and require solving complex nonlinear equations online at each time step, the proposed approach considers nonholonomic systems with both kinematics and dynamics, and generates gains through scalar differential equations. Meanwhile, the output-feedback case is also considered. This leads to a smooth and computationally efficient solution, significantly simplifying practical implementation. Additionally, we introduce dynamic gain scheduled strategies to adaptively adjust design parameters in real time, thereby enhancing the convergence rates of the closed-loop systems. As a practical application, we design a smooth time-varying dynamic gain scheduled control for an underactuated axisymmetric spacecraft system. The effectiveness of the proposed methods is demonstrated through comprehensive simulation results.

This study addresses distributed multivariate estimation and fault-tolerant control (FTC) for interconnected systems (ISs) subject to sensor and process/actuator faults under stochastic false data injection (FDI) attacks at interconnection nodes. A more general scenario is considered in which heterogeneous time-varying faults coexist in both sensor and process/actuator channels. A novel distributed robust multivariate observer (DRMO), incorporating two auxiliary variables and tunable estimation gains, is developed to simultaneously estimate subsystem states and heterogeneous fault signals. Consequently, a DRMO-based composite FTC scheme is proposed, which compensates for process/actuator faults, isolates sensor faults, attenuates FDI attacks, and stabilizes the overall system. Two root-mean-square gain performance indices derived using the proposed auxiliary functions guarantee robust performance of the multivariate estimation errors and system states in the presence of FDI attacks and other uncertainties, without imposing zero initial conditions. Finally, two simulation studies demonstrate the effectiveness of the proposed method.

The trajectory tracking control problem of unmanned surface vehicles(USVs)with unknown stochastic environmental disturbances was studied.Firstly,based on the theory of stochastic differential e-quations,a system dynamic model incorporating stochastic disturbance terms is established to accurately characterize the influence of environmental disturbances on the USVs motion trajectory.Secondly,a ro-bust trajectory tracking controller is designed based on the backstepping control method.The designed controller can ensure that the actual trajectory of the USVs asymptotically tracks any given reference traj-ectory with the desired precision.Then,it is rigorously proven that all signals in the closed-loop system satisfy global uniform ultimate boundedness.Finally,numerical simulations are conducted to verify the ef-fectiveness and robustness of the trajectory tracking controller.

We present novel prescribed-time (PT) output-feedback designs for stochastic nonholonomic systems. In contrast to existing designs, which typically assume known growth rates and guarantee only asymptotic performance, our designs achieve convergence within a user-specified time, regardless of the initial conditions-even when the growth rates are unknown. With the effect of stochastic noise, how to fully explore the blow-up function and the information of u0 to construct a new observer and a novel output-feedback control u1, to effectively deal with the u0-coupled nonlinear terms and to achieve PT convergence, is a challenging problem. Our control scheme ensures that the system states, observers, and controllers converge to zero within the same prescribed time. Finally, we use a kinematic cart to illustrate the PT output-feedback control designs. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

In this paper, the bipartite synchronization problem of coupled neural networks with sign-switching topology under replay attacks is investigated based on multi-rate sampled-data control. First, an error system model incorporating a Laplacian matrix coupling term is constructed based on graph theory and the properties of the switching topology. Second, a pinning multi-rate sampled-data controller is designed by incorporating the multi-rate sampled-data control scheme and the characteristics of replay attacks. Then, a looped-function that remains positive definite only at sampling instants is constructed. Considering the discrete-continuous Lyapunov stability theory and inequality techniques, a mean-square bipartite synchronization criterion is derived. Finally, the effectiveness and advantages of the control scheme and the constructed Lyapunov function are verified through numerical examples and the maximum allowable sampling interval algorithm.

This letter investigates the least-squares identification and adaptive control problem for stochastic high-order nonlinear systems. Noting that none of the existing adaptive designs on stochastic high-order nonlinear systems considers least-squares identification, the merits of our design are that all parameter estimates converge at similar rates, leading to more stable and predictable system behavior. Specifically, we first propose a novel least-squares identification method that uses an unfiltered regressor, then a new adaptive controller is designed to ensure that all system states converge to zero almost surely and that the closed-loop system is globally stable in probability. Moreover, by selecting appropriate estimator parameters, the convergence of the proposed estimator is ensured. Finally, two simulation examples, including Chua’s circuit system, are provided to validate the effectiveness of the proposed designs.

This paper investigates the prescribed-time formation control problem for the heterogeneous unmanned surface vehicles (USVs) under stochastic environmental loads. In real ocean environments, we consider the stochastic components of environmental loads to improve control performance, rather than regarding them as deterministic in previous research. A prescribed-time control strategy is introduced to achieve leader-follower formation control. We transform the prescribed-time formation control problem into an asymptotic convergence problem and design a prescribed-time formation controller by time-domain mapping and backstepping technology. Based on Lyapunov stability theory, we ensure that the formation tracking errors converge to a small value in probability within a prescribed time. The simulation results are provided to validate the effectiveness of the designed prescribed-time formation control method.

In this paper, a trajectory tracking control strategy for unmanned surface vehicles (USVs) with unknown time-variant disturbances is proposed. Firstly, in order to avoid the chattering phenomenon caused by unknown input interference, a hysteresis quantizer is introduced to quantize the input signals to filter out the influence of small fluctuations. Secondly, a disturbance observer is designed to estimate the unknown time-variant disturbances, and a quantized trajectory tracking control strategy based on the disturbance observer is proposed according to the Backstepping technique. Then, the stability of the closed-loop system is proved by using Lyapunov stability theory. Finally, the simulation results verify that the proposed control strategy can make the USV track the desired trajectory.

For linearly parametrized nonlinear systems in normal form, we first develop a new prescribed-time (PT) least-squares identification scheme (abbreviated PT-LS) characterized by a blow-up function, and then design a new PT adaptive controller which ensures that the plant state is regulated to zero in the prescribed time and the parameter estimate converges to a vector-valued constant in the same PT. Under a moderate interval excitation (IE) condition where the IE is fulfilled at the time strictly before the terminal time and we maintain the presence of IE in the estimator until the terminal time, even though the regressor may have lost the excitation, we redesign a new PT-LS estimator by introducing a novel term characterized by the blow-up function, online historical data and instant data, which not only ensures that the plant state is regulated to zero in PT, but also that the parameter estimation is strongly consistent in the same PT, i.e., the estimator PT-converges to the parameter's true value. Finally, two simulation examples are given to illustrate the PT-LS and adaptive control designs.

This paper proposes an adaptive prescribed-time quantized formation control method for the heterogeneous unmanned surface vehicles (USVs) under uncertain external disturbances. Different from the existing results, a prescribed-time formation controller is obtained indirectly by the time-domain mapping approach in the back-stepping control frame. To address uncertain external disturbances, the upper bounds of these disturbances are estimated using adaptive technology. Applying Lyapunov stability theory and input quantization technology, we ensure that the prescribed-time quantized formation controller can achieve formation stability in the prescribed time, and the formation tracking errors converge to a small neighborhood of zero. The simulation results demonstrate the efficacy of the designed formation control strategy.

For stochastic nonlinear multi-agent systems in strict-feedback form, we propose a novel distributed mean-nonovershooting control design under directed leader-followers type network topology. Compared with the existing stochastic distributed tracking control designs, the advantage of our design is that the leader's output can be tracked by the followers' outputs without any overshooting. Specifically, we first design new distributed controllers to ensure that the fourth-moment of the output tracking errors between the followers and the leader can be tuned arbitrarily small in the long run while all the states of the closed-loop system remain bounded in probability. Then we prove that the mean of the followers' outputs can asymptotically track the leader's output without overshooting if the initial values of the followers' outputs are suitably selected. Finally, a simulation example is given to illustrate the distributed mean-nonovershooting control design. (c) 2025 Published by Elsevier Ltd.

A novel distributed adaptive containment tracking control method is proposed for stochastic multiagent systems (MASs). Unlike existing results, we consider a more general system with both multiple dynamic leaders and unknown covariance. The control input of each agent system depends only on the states of its neighbors and its local states. When dealing with unknown time-varying covariance, we do not need to know its bound but use a proper estimation. Then, by using the backstepping design method, an adaptive law and a distributed adaptive tracking controller are designed. Using stochastic analysis and graph theory, it is proved that the outputs of the followers converge exponentially to the convex hull spanned by the outputs of the dynamic leaders under the condition that all signals of the closed-loop system remain bounded in probability and the tracking error is tunable. Finally, we illustrate the feasibility of the design scheme through numerical simulation.

This paper investigates the problem of nonovershooting tracking control of second-order nonlinear systems using sampled-data control. Firstly, by combining the Backstepping technique with sampled-data method, a sampled-data controller is constructed to ensure that all of the states are globally bounded and the tracking error between the system output and the reference signal can be made arbitrarily small. Then, based on the sampled-data controller, by suitably choosing the control gains and parameters, the output signal can track a given reference signal with an arbitrarily small amount of overshoot. Finally, a simulation example shows the effectiveness of the developed control strategy.

We present novel prescribed-time practical output tracking (PT-POT) designs for stochastic strict-feedback nonlinear systems. Compared with the existing stochastic nonlinear prescribed-time (PT) designs, there are two advantages in our design: the linear growth condition of drift terms and diffusion terms are completely removed; bounded control gains, instead of infinite control gains, are designed. We first design a new PT-POT controller, which ensures that the states and controller of the plant are bounded in probability, and the fourth moment of the output tracking error can be made arbitrarily small from the prescribed time on. Then we redesign a new inverse optimal controller and solve the prescribed-time practical inverse optimal tracking (PT-PIOT) problem, with an infinite gain margin. Specifically, the designed controller not only makes the fourth moment of the output tracking error arbitrarily small from the prescribed time on, but also optimizes a meaningful cost functional defined on the whole time domain. Finally, a simulation example is given to illustrate the stochastic nonlinear PT practical tracking designs.