In this paper, the problem of predefined-time adaptive event-triggered control of a class of nonlinear time-varying systems with full-state constraints and input saturation is investigated. By integrating the state-dependent function into the backstepping framework, the prerequisite feasibility assumption in traditional control methods is eliminated. Then, the challenges posed by unknown time-varying parameters and input saturation are handled through the introduction of auxiliary signals. Compared to existing studies, this paper proposes a unified adaptive event-triggered control framework that realizes the predefined-time steady-state control of time-varying systems under multiple constraints for the first time. The proposed control approach not only ensures the satisfactory control performance of the system but also significantly alleviates the transmission burden within the information channel. Finally, two simulation examples are presented to further demonstrate the effectiveness and practicality of the proposed control scheme.

This article investigates the problem of data-driven formation tracking control under distributed event-triggered mechanisms for underactuated unmanned surface vehicles (USVs) subjected to unmeasurable velocities and model uncertainties. Specifically, to address the issue of communication efficiency among formation members, a frequency-adaptive event-triggered mechanism is proposed. This event-triggered mechanism enables the adjustment of triggering frequency based on the magnitude of errors and accounts for the occasional communication instability in marine environments, while ensuring a minimum inter-event time. Second, a distributed reference state monitor (DRSM) under the novel event-triggered mechanism is developed based on local position information from neighboring USVs. The DRSM enables each USV to estimate its desired state information without relying on global path information. Furthermore, a data-driven dynamic control strategy is proposed based solely on position information. A neural-based data-driven controller is designed to estimate model uncertainties and unknown control input gains using real-time and historical data, without requiring prior knowledge of system parameters. Finally, the effectiveness of the proposed approach is validated through rigorous stability analysis and numerical simulations.

Sparse Bayesian learning achieves great success in damage identification by employing a sparsity-inducing prior distribution on the sparse coefficients. However, if the input force is unknown, a sparse prior cannot be applied to both the damage and force parameters. In order to construct a sparse Bayesian learning model for damage and unknown load input identification, a sensitivity-based sparse Bayesian method for the damage detection with unknown input is proposed. An optimization equation is constructed on the basis of the dynamic response sensitivity to convert the complex non-linear relationships into linear equations. The prior information for the force and damage parameters is established using uniform and Gaussian priors, respectively, depending on the specific characteristics of each parameter. The Bayesian learning framework based on the sensitivity-based model is derived to compensate the linear truncation errors and measurement noise. The validation of the proposed approach is conducted using both a numerical frame structure and an experimental structure. Results indicate that this method can simultaneously identify both damage and forces, even when faced with significant measurement noise and limited sensor data.

This paper investigates the issues of event-triggered bipartite consensus for multi-agent systems (MASs) with disturbances on uncertain Markovian switching topologies, where completely unknown transition rates are considered. All designs are carried out under the assumption that the agents' states cannot be measured, and each agent can only receive output information from its neighbours. Initially, a distributed consensus variable (DCV) is constructed for each agent so that the bipartite consensus problem reduces to the convergence of the DCV. Subsequently, the dynamics of the DCV are established and characterised as an uncertain system with an accumulated disturbance. Secondly, for the DCV dynamic system, a distributed interval observer (DIO) is designed. Based on the DIO, an algebraic correlation between the accumulated disturbance and the DCV is derived. Furthermore, by using the outputs from its neighbours, a distributed unknown input observer (DUIO) is developed for each agent, which provides asymptotically converging estimates of the DCV and the accumulated disturbance. Thirdly, for the DCV system, a DUIO-based event-triggered control protocol is developed that guarantees the asymptotic stability of the DCV dynamic system. In this way, bipartite consensus for MASs is achieved. Finally, the effectiveness of the proposed method is validated through a simulation example.

Ensuring safe driving requires continuous monitoring of both vehicle dynamics and external conditions such as road irregularities, which often act as unknown disturbances. Accurately estimating these unmeasured states and inputs is critical for advanced driver assistance systems (ADAS) and vehicle stability control. This study proposes a novel functional observer that simultaneously reconstructs unknown road disturbances and estimates unmeasured vehicle-state variables in real time using only standard onboard sensor measurements. The observer design is grounded in Lyapunov stability theory, with estimation conditions expressed as linear matrix inequalities (LMIs), whose solution guarantees robust convergence and stability. Validation is conducted through numerical simulations of a quarter-car vertical dynamics model under two scenarios. Results demonstrate that the proposed observer achieves accurate and reliable state estimation, outperforming conventional approaches such as the Kalman filter and full-order Luenberger observer, particularly in the presence of unknown inputs.

Distributed State Estimation for Discrete-Time LTI Systems in the Presence of Unknown Inputs

Self-triggered secure bipartite formation for MASs against byzantine attacks: A distributed unknown input observer approach

This paper addresses the event-triggered distributed prescribed performance consensus control problem for uncertain nonlinear multi-agent systems subject to unknown input saturation and control direction. To address system uncertainties, we estimate unknown nonlinear functions through the universal approximation capability of neural networks. Furthermore, Nussbaum-type functions are utilized to concurrently handle the unknown saturation and control direction. Considering that the communication resources may be limited, a dynamic event-triggered mechanism is constructed. Unlike existing relative-threshold-based approaches, an adaptive threshold is designed based on consensus error to ensure event-triggered communication. Meanwhile, a prescribed performance framework is employed to ensure the consensus error remains strictly bounded. Building upon these techniques, a distributed event-triggered consensus control strategy with prescribed performance is developed. Its theoretical feasibility is rigorously verified using Lyapunov stability theory, and two simulation examples are finally provided to demonstrate the effectiveness of the proposed strategy.

To address compound faults—including actuator faults, sensor faults, and unknown disturbances—in the main drive system (MDS) of a rolling mill, a fault diagnosis model is established based on the d-q model of a three-phase AC motor. To overcome the limitation of conventional model-based fault detection (MFD) in isolating faults under compound fault scenarios, a novel fault diagnosis framework is proposed by integrating model residuals with deep learning. An Unknown Input Observer (UIO) is designed to detect system faults, and its convergence is rigorously proven using Lyapunov theory and linear matrix inequalities (LMIs). The coupled residual signals generated by the observer are segmented into sequential subsequences and processed by a Convolutional Neural Network (CNN) for feature extraction and classification. To account for the temporal and dynamic nature of the residuals, a Tyrannosaurus Rex Optimization Algorithm (TROA) is adopted to optimize the CNN hyperparameters. Numerical simulations on a rolling mill demonstrate that the proposed UIO achieves superior state estimation performance, with a 16.48% reduction in the Root Mean Square Error (RMSE) of angular velocity difference of the motor compared to the Sliding Mode Observer (SMO). Furthermore, the proposed TROA-CNN outperforms Bayesian Optimization (Bayes)-CNN, Whale Optimization Algorithm (WOA)-CNN, and Grey Wolf Optimization (GWO)-CNN in terms of fault classification accuracy (99.76%) and noise robustness (96.27% under 5% noise). In scalability tests where the number of fault types or dataset size are doubled, the inference latency increases by approximately 10%, and the training time rises by about 40%. These results demonstrate that the UIO-TROA-CNN achieves high accuracy, strong robustness, and excellent scalability, making it well-suited for fault diagnosis in industrial environments with high noise and complex fault types.

This paper proposes a novel distributed attack detection framework for large-scale systems (LSSs), with a specific focus on low-voltage direct current microgrids (DC MGs). The architecture integrates two complementary detection modules: an event-triggered (ET) observer for local subsystem monitoring and a set of distributed unknown input (UI) observers for assessing the states of neighboring subsystems. To enhance robustness against disturbances, an adaptive compensation mechanism is incorporated. The framework supports an ET control strategy designed to ensure consensus performance, prevent Zeno behavior, and reduce communication overhead. Additionally, a fault detection method based on the state observer is introduced to identify faults within subsystems in real time. The proposed detection method is validated through detailed simulations that consider process noise, model uncertainties, and multiple attack scenarios, including false data injection, stealth, and replay attacks. Results demonstrate that the integrated detection units significantly improve resilience by identifying attacks that would otherwise remain undetected by standalone modules. The study assumes ideal communication links and bounded model uncertainties. Future work aims to address non-ideal communication conditions, investigate time-varying topologies, and develop autonomous reconfiguration strategies based on plug-and-play control.

This paper deals with the problem of designing unknown input observers for a class of coupled semilinear wave partial differential equations (PDE) systems. A state observer is designed to estimate the uncertain coupled wave PDE systems. Then the analysis of the asymptotic stability and H ∞ performance for the observer design of coupled wave PDE systems is investigated. Some sufficient conditions of asymptotic stability for the observer error system with disturbance attenuation level are derived via matrix inequalities based on the Lyapunov stability theory. Finally, a numerical simulation is presented to demonstrate the effectiveness of the obtained result.

ABSTRACT This paper investigates a global prescribed‐time trajectory tracking control problem for a quadrotor unmanned aerial vehicle (QUAV) subject to non‐vanishing uncertainties. To overcome the limitations of traditional prescribed‐time control (PTC) methods that rely on switching mechanisms or are sensitive to initial conditions, a novel prescribed‐time controller is constructed based on reference convergence differential functions (RCDF), avoiding any state transition and reducing computational burden. To the authors' best knowledge, while many existing PTC methods can handle non‐vanishing uncertainties (NVU), effectively addressing NVU in under‐actuated systems remains a challenging issue. Then, a prescribed‐time unknown input observer (PTUIO) is designed to estimate translational disturbances, and an adaptive law is introduced into the attitude subsystem to compensate for NVU. Moreover, this control strategy guarantees the system convergence over the entire time interval with a user‐defined settling time, regardless of initial conditions. Simulation results under various conditions demonstrate the effectiveness, robustness, and practical feasibility of the proposed scheme compared to related methods.

Understanding the neural mechanisms underlying the transitions between different states of consciousness is a fundamental challenge in neuroscience. Thus, we investigate the underlying drivers of changes during the resting-state dynamics of the human brain, as captured by functional magnetic resonance imaging (fMRI) across varying levels of consciousness (awake, light sedation, deep sedation, and recovery). We deploy a model-based approach relying on linear time-invariant (LTI) dynamical systems under unknown inputs (UI). Our findings reveal distinct changes in the spectral profile of brain dynamics-particularly regarding the stability and frequency of the system's oscillatory modes during transitions between consciousness states. These models further enable us to identify external drivers influencing large-scale brain activity during naturalistic auditory stimulation. Our findings suggest that these identified inputs delineate how stimulus-induced co-activity propagation differs across consciousness states. Notably, our approach showcases the effectiveness of LTI models under UI in capturing large-scale brain dynamic changes and drivers in complex paradigms, such as naturalistic stimulation, which are not conducive to conventional general linear model analysis. Importantly, our findings shed light on how brain-wide dynamics and drivers evolve as the brain transitions toward conscious states, holding promise for developing more accurate biomarkers of consciousness recovery in disorders of consciousness.

Distributed output-feedback optimization for uncertain nonlinear multi-agent systems with unknown input delay

A Data Centric Approach to the Design of Unknown Input Functional Observers

This paper develops a novel fault reconstruction (FR) method and an FR-based fault-tolerant control (FTC) scheme for systems suffering from both sensor and actuator faults based on the combination of a Luenberger-like reduced-order observer and an interval observer. Firstly, by introducing an output transformation, an auxiliary output that is able to decouple the sensor fault is obtained. Secondly, for addressing the external disturbance and actuator fault, a multiple unknown input (MUI) is formed, and a reduced-order observer that is able to decouple the MUI is constructed. Consequently, asymptotic convergence estimations of the state and the sensor fault can be accomplished. Thirdly, in order to obtain the asymptotic convergence actual FR (AFR), an interval observer is designed. After this, an algebraic connection of the MUI and the state error estimation is given, and, based on the algebraic relationship, an algebraic MUI reconstruction (MUIR) method is proposed. Finally, an FTC scheme is developed by using the state estimation and MUIR. Under the FTC, the closed-loop system is asymptotically stable even if it suffers from sensor and actuator faults simultaneously. Theoretical analysis demonstrates that the observer-based FTC mechanism satisfies the separation principle. At last, two simulation examples are given to verify the effectiveness of the proposed methods.

In this paper, we propose a method for identification of continuous-time fractional-order systems with unknown states and input delays. In practice, many systems are modeled accurately with fractional differential equations. In particular, many systems are modeled as fractional differential equations with input delay and state delay. Since the geometric and physical meaning of fractional calculus is not clear, it is difficult to model the real system directly to fractional order systems based on mechanical analysis. Thus, the identification of fractional order systems is the main method for constructing fractional order models and is the subject of the main research by many scientists. To solve the identification problem of systems with input delay and state delay, we use the fact that the fractional integral operator matrix by the block pulse functions is an upper triangular Toeplitz matrix. We have presented an efficient method to identify the linear and nonlinear parameters separably by using the commutativity and nilpotent property for multiplication between upper triangular Toeplitz matrices. We also have presented an efficient algorithm to newly approximate the Jacobian of the variable projection functional to solve the least squares problem with nonlinear parameters. Several simulation examples have been used to verify the effectiveness of the proposed method. It is shown that the input delay and the state delay have a significant effect on the output characteristics of the system, especially the state delay has a larger effect than the input delay.

This paper investigates the potential of utilizing frequency-varying negative stiffness properties of the inerter in vehicle suspensions to improve the comprehensive dynamic performance. Firstly, the dynamic characteristics of the air spring and the inerter are analyzed to evaluate the feasibility of integrating them into vehicle suspensions. Secondly, a quarter-vehicle model incorporating the nonlinear stiffness features of an air spring is established, and a vehicle semi-active control strategy for the air inerter–spring–damper (ISD) suspension based on the frequency-varying negative stiffness of the inerter is proposed. Thirdly, in order to implement this strategy effectively, this paper builds an uneven road surface estimator based on the discrete Kalman filter with unknown input (DKF-UI) and an uneven road surface frequency identifier based on the first order-zero crossing algorithm. Finally, the superiority of the proposed suspension system is verified by simulations, and the results reveal that with respect to the passive air suspension, the peak values of the gains of the body acceleration, the suspension working space and the dynamic tire load are reduced. The vehicle semi-active air ISD suspension exhibits reductions of 68.7%, 51.0%, 67.6% in the body frequency region and 5.1%, 9.9%, 7.9% in the wheel frequency region, respectively. Under a segment sinusoidal road input, the RMS values of the three performance indicators exhibit reductions of 79.2%, 57.8%, 77.7% at 1.4 Hz and 6.8%, 15.4%, 5.8% at 11 Hz, respectively. Consequently, the vehicle semi-active air ISD suspension proposed in this paper has significant performance improvement at both the vehicle body natural frequency and the wheel natural frequency region compared to the passive air suspension, which indicates that it has better ride comfort and road holding performance.

A novel nonlinear decoupling approach to design unknown input observer for active vehicle suspension system

Research on attack detection and state estimation for distribution networks based on sparse recovery and unknown input observer