This article explores an event-triggered self-learning parallel tracking control strategy for continuous-time nonlinear systems with actuator faults. To mitigate the impact of actuator faults, an enhanced performance index function is developed based on the unknown upper bound of such faults. Furthermore, an augmented error nonlinear system is constructed by incorporating the tracking error and control input of the original system, so as to implement parallel tracking control via the adaptive dynamic programming (ADP) approach. By designing an adaptive law, the unknown upper bound of faults is estimated online, which adjusts the control parameters in real-time and compensates for the loss of control effectiveness induced by faults. A critic network is employed to approximate the optimal value function within an event-triggered framework, while a dynamic triggering mechanism is adopted to reduce communication overhead. Through the design of appropriate Lyapunov functions, the asymptotic stability of the closed-loop system is rigorously proven, and the weight estimation error is demonstrated to be uniformly ultimately bounded (UUB). Finally, the simulation results are provided to validate the effectiveness of the proposed control strategy.
This work investigates the zero-error tracking problem for linear systems with unknown dynamics. The proposed method integrates a data-driven system model with an auxiliary system for error characterization. First, a nonminimal state-space (NMSS) model is constructed from historical input-output data. Then, an auxiliary system is formulated by leveraging the common minimal polynomial shared by the disturbance and reference trajectory. The stabilizability and detectability of the auxiliary system are rigorously verified, thereby guaranteeing the existence of a unique positive semidefinite solution to the Riccati equation. Inspired by reinforcement learning (RL) principles, a data-driven output-feedback optimal tracking controller is developed by iteratively learning the optimal Q-function. The theoretical superiority of the proposed controller over existing approaches is established. Simulation results further demonstrate its effectiveness in addressing the tracking problem subject to measurement delays and unmeasurable disturbances.
Safe trajectory tracking for nonlinear stochastic systems operating in obstacle-cluttered environments remains a significant challenge, as random disturbances and obstacle-induced constraints can simultaneously degrade tracking accuracy and threaten system safety. To overcome this issue, this article develops a safety-aware optimal tracking control framework that integrates stochastic control barrier functions (CBFs) with adaptive dynamic programming (ADP) for obstacle avoidance. To ensure safety, a logarithmic-type stochastic CBF is constructed to enforce obstacle-avoidance constraints, and theoretical guarantees are provided for the stochastic forward invariance (SFI) of the safe set. Furthermore, based on the integral reinforcement learning (RL) framework, an ADP algorithm is developed to relax the need for system dynamics. A critic-only neural network (NN) scheme is employed to approximate the solution of the Hamilton-Jacobi-Bellman (HJB) equation, with a fixed-time weight update rule established to guarantee convergence independent of initial conditions. Meanwhile, an experience replay mechanism is incorporated to relax the persistent excitation condition. It is further shown that the estimation error of the NN weights is fixed-time stable (FxTS). Finally, simulation results demonstrate that the designed method achieves optimal trajectory tracking while ensuring safety under stochastic dynamics, even in scenarios involving multiple obstacles.
Because of the similar structures and motion mechanisms between pneumatic artificial muscles (PAMs) and biological muscles, PAM-actuated wrist joints exhibit substantial potential for applications in rehabilitation and industrial fields. Nevertheless, the complex nonlinearities, hysteresis, and creep inherent in PAMs bring significant challenges to precise motion control. Moreover, the material compliance and limited motion ranges of PAMs make it difficult to guarantee the safe operation of multi-PAM-actuated robots. To this end, a new iterative learning control (ILC) method is investigated to accomplish the efficient tracking control of PAM-actuated wrist joints. Without complex modeling work, ILC is introduced to estimate iteration-invariant dynamic model parameters. In particular, the identical initial condition in traditional ILC is relaxed by implementing a trajectory reconstruction mechanism. Also, a tanh-type adaptive law is designed to estimate the upper bounds of the lumped disturbances without prior knowledge. Moreover, an asymmetric time-varying barrier Lyapunov function (BLF) is utilized, ensuring that the tracking errors are maintained within permissible limits. The convergence of the proposed control method is demonstrated in both the time and iteration domains. Eventually, the effectiveness and superiority of the control method are validated via experiments.
In this study, the event-triggered distributed Kalman consensus filtering problem for multitarget tracking systems vulnerable to malicious attacks is the main topic. Based on the directed network topology, the coupled measurement that relies on target states from incoming neighborhoods is utilized to estimate the target state. Considering the coupling features of measurements, an augmented-system method is introduced to reconstruct the system model. Due to the constraints of communication bandwidth and vulnerability of the communication network between filters, an event-based distributed Kalman consensus filter (DKCF) is designed under cyberattacks. For scalability considerations, a suboptimal DKCF is derived by simplifying the optimal one. To analyze the tracking performance of the proposed suboptimal DKCF, a sufficient condition is devised to ensure its stability, and the consensus gain matrix is subsequently obtained. Moreover, the relationship between the attack vector and the event-triggered method is established, and a feasible event condition in a practical environment is derived. Finally, to confirm that the event-based DKCF mentioned above is effective, a multitarget tracking system simulation example is provided.
Anomaly detection (AD) has attracted increasing attention because of its importance in identifying unusual patterns across widely applications. Existing reconstruction-based AD methods have shown strong capability in modeling complex data distributions, but still face several limitations. First, most methods assume that the training data contain exclusively of normal samples (normals), limiting their applicability in practical scenarios. Second, redundant and irrelevant features in high-dimensional data weaken the discriminative capability of learned representations. Therefore, we propose a representation-enhanced AD model with prototype learning and neighborhood rough set (ADPLN). Specifically, a neighborhood rough set (NRS)-based feature selection strategy is employed to identify informative features for more discriminative representations. An adaptive prototype learning mechanism is introduced to adaptively represent diverse normal patterns. Furthermore, we design a sample-prototype correlation objective function to promote the learning of discriminative representations of normals and mitigate the negative impacts of anomalies. Extensive experiments on 13 real-world datasets demonstrate that ADPLN outperforms the state-of-the-art methods.
In this article, a spatiotemporal recognition model was proposed to nondestructively map the geological condition of metro tunnel, avoiding the low generality problem of the existing machine learning (ML) methods operating on the correlative dynamic parameters of inaccuracy theory. Specifically, first, a temporal estimator based on weighted least square method (WLSM) is designed to calculate stratum thickness from posterior estimations, and its static weight as input control corrects the direction and speed of geology evolution according to observation, copying with non-Gaussian noises while avoiding the oversimplification error of extended Kalman filter (EKF). Second, a spatial observer based on geomechanical theory simulates ladder-dimensional unscented Kalman filter (UKF), matching the nonlinear geological models while reducing the computation and initialization complexity of UKF through ladder-dimension sigma sampling points. Third, the input control parameter is refined by a back propagation neural network (BPNN) improved to reduce learning time through exponentially extending the learning rate and constraining the initial learning values. Finally, theory proofs and experiment comparisons are conducted to verify its accuracy and cost.
Stability is a prerequisite for safe and reliable system operation; however, time-varying input delays (TVIDs) and unknown nonlinearities pose significant challenges for stable control. To overcome these challenges, a predictor-based adaptive neural network control method is proposed. First, to mitigate the adverse effects of TVIDs on control performance, an observer-form predictor (OFP) is constructed, and a corresponding state feedback control strategy is designed. Second, a radial basis function neural network (RBFNN) with the predicted state as input is employed to approximate the unknown system nonlinearity and eliminate acausality in the controller and OFP. Third, to improve control performance, a prediction error compensation term is added to the OFP-based controller. Furthermore, a Lyapunov-Krasovskii (L-K) functional is designed for stability analysis, and less conservative sufficient conditions (SCs) are derived based on the generalized free-weighting matrix inequality (GFMI). Finally, simulation examples are provided to verify the effectiveness of the proposed method.
Existing multiobjective evolutionary algorithms (MOEAs) struggle to simultaneously achieve high-precision approximation of the Pareto front (PF) and effectively identify all Pareto subsets in the decision space. To address this issue, this article proposes a multimodal multiobjective particle swarm optimization (MOPSO) algorithm based on special crowding distance (SCD) and a modality-aware strategy (MMOPSO_SCDMA). The algorithm designs an SCD that simultaneously quantifies the distribution density of individuals in both the decision space and the objective space, employing a dynamic threshold selection strategy to balance diversity across the two spaces. An adaptive-parameter DBSCAN algorithm periodically clusters the external archive (EA) to construct a global leader set (GLS), while in nonclustering phases a reference point method generates a local leader set (LLS), thereby achieving a dynamic balance between coarse-grained exploration and fine-grained exploitation. In addition, a boundary-distance-sensitive mutation operator is introduced, which dynamically adjusts the perturbation intensity according to the particle position, effectively mitigating premature convergence. The experimental results on 20 test functions from the MMF and MMMOP benchmarks demonstrate that MMOPSO_SCDMA significantly outperforms 11 existing state-of-the-art algorithms across multiple performance metrics.
This article investigates the stealthy attack design against the sequential estimation of cyberphysical systems (CPSs), with the aim of providing a theoretical basis for refining defense mechanisms. A multiobjective attack model is proposed under the energy constraint, which comprehensively utilizes available innovations from both reliable and suspicious sensors to disrupt the state estimation performance with the assurance of stealthiness. By deriving the recursion of the error covariance, the optimization objective is formulated as a tradeoff between the terminal and average estimation errors to accommodate different scenarios. The corresponding stealthiness conditions are further analyzed based on an analysis of the statistical characteristics of coupled innovations. Then, according to the properties of orthogonal matrices and the Lagrange multiplier method, closed-form solutions for the optimal attack matrices are derived, which avoid addressing the semidefinite programming problem. Moreover, the optimal scheduling is solved via 0-1 programming after parameter separation. Finally, numerical simulations are provided to validate the results.
This article focuses on the scaled consensus problem of time-scale-type multiagent systems (MASs) under communication networks subject to denial-of-service (DoS) attacks. A dual-channel dynamic event-triggered mechanism (DETM) is proposed to reduce both actuator update frequency and communication overhead. By constructing a nonnegative function integrated with time-scale calculus theory, sufficient conditions are derived to guarantee the scaled consensus while excluding Zeno behavior. The conclusions derived from this method can be applied to MAS models in both continuous and discrete time domains. Finally, a numerical simulation and a case study on autonomous marine vehicles (AMVs) are presented to validate the effectiveness and feasibility of the proposed approach.
This article investigates the design of stealthy false-data injection attacks against distributed Kalman consensus filtering (KCF) over wireless sensor networks. This attack aims to maximize the degradation of remote state estimation performance under a stealthiness constraint quantified by the Kullback-Leibler (K-L) divergence. Most existing literature concentrates on centralized estimation schemes, while the proposed framework targets transmitted innovation channels in distributed KCF and fully accommodates topology-induced structural constraints. A historical innovation-driven linear attack model is formulated to leverage temporal innovation data, enlarging the feasible stealthy attack region compared to what is afforded by traditional memoryless innovation-based adversarial schemes. The resulting worst case attack design is reformulated into a relaxed optimization problem at the covariance level. The least-favorable attacked innovation is verified to follow a Gaussian distribution, which enables the closed-form characterization of the unconstrained worst case covariance. To enforce the block-diagonal constraint induced by network topology, a projected gradient descent (PGD) algorithm is developed to synthesize topology-feasible attack gains for distributed practical implementation. Finally, numerical simulations validate the theoretical analysis and demonstrate the effectiveness of the proposed attack scheme.
In this study, we propose an incrementally expanding fuzzy neural module network (FNMN) designed to effectively handle both low- and high-dimensional problems without relying on dimensionality reduction techniques. The proposed framework adopts a modular and hierarchical architecture, in which univariate fuzzy neural modules (UFNMs) are incrementally selected and connected according to their representational capability, quantified by the coefficient of determination. The variable-specific univariate fuzzy rule architecture avoids exponential rule growth while preserving interpretability. A residual-driven hierarchy incrementally selects informative modules and progressively refines the model. A hybrid learning strategy combines efficient modulewise learning based on least squares error estimation with global fine-tuning via backpropagation (BP). Adam-based optimization is adopted to enhance convergence stability and reduce sensitivity to learning-rate settings. Extensive experiments on 28 publicly available benchmark datasets demonstrate the effectiveness of the proposed approach. The proposed method achieves an average performance improvement of 19% compared with a conventional fuzzy clustering-based model across diverse benchmarks. Statistical significance tests further confirm that the proposed model significantly outperforms recent neurofuzzy systems. Notably, competitive predictive performance is attained while model complexity is reduced by more than two orders of magnitude relative to deep learning approaches. These findings highlight the efficiency and scalability of the proposed framework.
This article addresses the secure consensus problem of Takagi-Sugeno (T-S) fuzzy multiagent systems (MASs) under replay attacks through event-based asynchronous control. Different from the existing research on event-triggered schemes (ETSs), a novel adaptive parallel-triggering strategy is designed to efficiently utilize limited network bandwidth and flexibly cope with system state changes. To deal with cybersecurity threats and complex nonlinear problems, a novel security consensus model for MASs under replay attacks based on the T-S fuzzy model is proposed. Then, the concern of asynchronous premise variables is addressed. Theoretical foundations are established via Lyapunov-Krasovskii-based stability analysis, yielding a set of verifiable secure control criteria that guarantee leader-following consensus under replay attacks. Comparative numerical simulations demonstrate the proposed method's superiority over conventional triggering schemes in both security performance and resource efficiency, validating the theoretical advancements.
Cyber-physical systems (CPSs) are increasingly integral across modern industries, yet malware proliferation poses significant challenges to their security and stability. This study introduces an advanced model for malware spread that leverages Turing instability and fractional-order diffusion, offering insights into malware propagation dynamics. By developing a 2-D susceptible-infected (SI) model with both self-diffusion and cross-diffusion, we explore the nonlinear interactions influencing malware propagation across CPS nodes. Fractional-order diffusion models are also employed to represent complex, nonlocal propagation, while a state feedback controller is incorporated to manage malware dynamics effectively. The study details conditions for Turing bifurcation and bifurcation thresholds, revealing that changes in the bifurcation parameter influence pattern formations, shifting from hexagonal to stripe formations in malware-infected nodes. Our simulations validate these theoretical insights, demonstrating that the controller and fractional-order diffusion significantly impact malware propagation patterns. This model offers a novel framework for developing malware diffusion control strategies, enhancing cybersecurity resilience in CPSs.
The interconnected RLC circuits are essential nonlinear models for analyzing dynamic coupling and energy transfer in complex electrical networks, serving as a standard testbed for nonsmooth control, time-delay analysis, and synchronization theory research. However, the existing theoretical studies exhibit prominent limitations: most works ignore the dimensional heterogeneity between drive Cresponse circuit subsystems and fail to integrate neutral time delays and Filippov nonsmooth characteristics in system modeling. Moreover, the coordination mechanism between dynamic event-triggered control and indefinite-function-based stability analysis remains underexplored, and incomplete Lyapunov derivative definiteness verification restricts the accuracy and generality of the existing synchronization criteria. Addressing these theoretical gaps, this article investigates the fixed-time (FxT) synchronization control of networked neutral Filippov systems with heterogeneous dimensions. A comprehensive system model is constructed to accommodate dimensional mismatch, neutral time delay, nonsmooth Filippov dynamics, and event-triggered control coupling. Specifically, a novel FxT stability lemma for indefinite functions is proposed to compensate for the defects of conventional Lyapunov analysis methods. Combined with nonsmooth analysis and state-space reconstruction, a rigorous synchronization error model is established for dimension-mismatched systems. Meanwhile, the static and dynamic event-triggered control strategies are designed to reduce network resource consumption, with the strict positivity of dynamic triggering functions theoretically proven. Finally, numerical simulations on mismatched RLC circuit systems validate the effectiveness and superiority of the proposed unified FxT synchronization framework.
Consensus is a crucial issue for Euler-Lagrange multiagent systems (MASs) and their communication resources are often limited. Thus, this article is focused on the leaderless consensus of Euler-Lagrange MASs with limited communication resources. First, a distributed event-triggered (ET) control protocol is proposed, in which the information in both the agent's internal sensor-controller channels and the external channels among agents update only at discrete triggered instants. Compared with existing control protocols, the ET-based distributed control protocol can considerably reduce the transmission loads for Euler-Lagrange MASs. Second, a new method for exclusion of Zeno behavior is proposed, in which only the local Lipschitz condition of systems parameters is needed, and the differential mean value theorem (DMVT) and the boundedness of a continuous function on a closed interval are mainly used. Compared with existing constraint conditions, the differentiability of the agent's regressor matrix is removed. Then, by the ET-based distributed control protocol, leaderless consensus results are derived for Euler-Lagrange MASs. Finally, based on networked two-linked robot manipulators, simulations are presented to show the validity and less communication utilization of the proposed results.
This article develops a practical fixed-time tracking control framework for a class of strict-feedback nonlinear systems subject to unknown external disturbances. A fixed-time disturbance observer (FxTDO) is first designed to reconstruct the disturbances together with their higher-order derivatives within a uniform settling time whose upper bound is independent of the initial conditions. To avoid the explosion of complexity arising from the repeated differentiation of virtual controllers, a fixed-time command filter (FxTCF) is incorporated into the recursive backstepping design. In contrast to conventional command filters with persistent filtering errors, the proposed FxTCF guarantees that the filtering error vanishes within a fixed time. A switching function is further embedded into the virtual control laws to ensure the required second-order differentiability and enable the effective implementation of the FxTCF without introducing additional error compensation dynamics. Moreover, a dynamic event-triggering mechanism is integrated into the control framework to reduce unnecessary transmissions while preserving the desired closed-loop performance. Theoretical analysis establishes the boundedness of all closed-loop signals, the practical fixed-time convergence of the tracking error to a prescribed residual set, and the exclusion of Zeno behavior. Simulation results for a flexible robotic manipulator demonstrate the effectiveness and advantages of the proposed control framework.
