System State Estimation Research Articles

Zonotopic set-membership state estimation for nonlinear systems based on the deep Koopman operator

In this study, a novel nonlinear zonotopic set-membership estimation (SME) approach is proposed based on the Koopman operator and the deep neural networks (DNNs). The core concept involves transforming the original nonlinear system into a higher-dimensional linear system, enabling the development of linear SME algorithms. To address noise in real-world data, we propose a three-step offline training strategy for computing the linear approximation of nonlinear dynamics. Building on the deep-Koopman-based linearized system, we construct a reduced-order filter structure that directly estimates the original states and then computes the lifted states for improved observability. We derive two optimal gains based on different size criteria and present a data-driven nonlinear mapping approach that ensures a closed-form solution for the algorithm. Additionally, we introduce a local model update method that refines estimation accuracy using the set of state estimates obtained from SME. The effectiveness and superiority of our proposed methods is demonstrated through two illustrative examples.

A Method to Handle Unbalanced Systems in Branch Current-Based State Estimators

The undergoing energy transition to a sustainable future requires, among other things, the application of demand side management (DSM) techniques to maintain grid stability and allow a smooth performance. To successfully implement DSM strategies, near real-time monitoring of the grid is required. This can be achieved through a distribution system state estimator (DSSE). Conventional approaches to state estimation (SE) typically rely on the assumption of a balanced reference bus, which is reasonable for transmission systems but may not be applicable to low-voltage distribution networks, even more with significant distributed generation (DG) penetration. To address this problem, a branch current-based low-voltage DSSE for unbalanced three-phase systems is developed. The algorithm incorporates a virtual bus to account for highly unbalanced systems, enabling it to obtain a more accurate estimation of the grid state. The proposed method is compared to the conventional balanced reference bus method through multiple simulations under different load conditions in the IEEE European low-voltage test feeder.

Charge diagnostics and state estimation of Battery Energy Storage Systems through Transformer models

Charge diagnostics and state estimation of Battery Energy Storage Systems through Transformer models

Robust Kalman filtering with Moving Horizon Estimation and multivariate Laplace modeling

This study introduces a novel approach for state estimation in linear systems impacted by measurement outliers. By analyzing measurement information within a time window, the method enhances measurement utilization efficiency, leading to more accurate identification and mitigation of outliers. Noise is modeled as a Multivariate Laplace (ML) distribution, which effectively avoids the complexity of estimating the degrees of freedom (DOF) parameter. Moreover, the integration of the Variational Bayesian (VB) method with Moving Horizon Estimation (MHE) enables joint inference of unknown parameters, increasing the flexibility and accuracy of the noise model while improving the system’s robustness against outliers. Simulation results show that the proposed algorithm outperforms existing methods in both effectiveness and robustness when handling outliers.

Influence of the degree of meshing on the observability and reliability of monitoring systems for power system state estimation

Influence of the degree of meshing on the observability and reliability of monitoring systems for power system state estimation

Sliding Mode Fault-Tolerant Control for Nonlinear High-Order Fully Actuated Systems.

The high-order fully actuated systems (HOFASs) approach can only completely eliminate known nonlinearities. However, the practical systems often encounter unknown nonlinearities, including disturbances and faults. Therefore, this article studies a class of nonlinear HOFAS with component faults and disturbances. By applying the HOFAS theory, a novel integrated sliding mode fault-tolerant control strategy is proposed to ensure the stability of the closed-loop system. The state feedback and output feedback controllers are designed, respectively. For output feedback control, an extended state observer is designed to estimate system states. Once the HOFAS model is established, the designed controller and extended state observer can be directly implemented, facilitating the analysis and design of the control system. And the stability analysis does not depend on the complexity of the nonlinear functions. Finally, a numerical simulation example shows the effectiveness of the proposed method.

Improving distribution system state estimation: novel metadata driven approach for pseudo measurement generation

Improving distribution system state estimation: novel metadata driven approach for pseudo measurement generation

Analysis of observability and detectability for CSTR model of biochemical processes under uncertain system dynamics and various sets of measured outputs

An analysis of observability and detectability for continuous stirred tank reactor model of selected biochemical processes has been addressed in this paper. In particular, properties of observability or detectability of the considered system model have been proved under uncertain system dynamics in view of various sets of system measured outputs. It is related to considering system dynamics depending on initial conditions and the impact of inputs taking into account a given measured output. The method of indistinguishable state trajectories (indistinguishable dynamics) and tools based on the Lyapunov second method were used to investigate the observability and detectability properties. The analysis was performed for eight cases of different sets of measured outputs with association to the realistic features of measuring devices. The obtained research results are essential for system state estimation that involves the synthesis of state observers. The proposed approach may be successfully applied to the complex biochemical non-linear uncertain systems modelled as continuous stirred tank reactors.

Development of an Extended State Observer for Monitoring of a PWR Based on a Two-Point Kinetic Model

Accurate estimation of unmeasured system states and disturbances in a pressurized water reactor (PWR) is essential for effective control, operation optimization, and safety monitoring. To this end, this paper investigates the estimation of unmeasured system states and disturbances of the PWR system during load-following operation. First, a mathematical model for the PWR system is established based on the two-point kinetics equations with one equivalent delayed neutron precursor group. Subsequently, an extended state observer (ESO) integration scheme, incorporating two coupled ESOs, is constructed to estimate unmeasured system states, including relative density of delayed neutron precursor, average fuel temperature, total reactivity, xenon concentration, and iodine concentration, along with time-varying disturbances, with the use of measurements of the PWR system only. According to the Lyapunov stability theorem, it is proved that the estimation error dynamic of the proposed ESO integration scheme is uniformly ultimately bounded stable. Finally, simulation results confirm that the proposed ESO integration scheme provides higher estimation accuracy and stronger robustness against measurement noises, model uncertainties, and external disturbances compared to both a high-gain observer and a high-order sliding mode observer.

Adaptive proportional integral derivative fault tolerant control for continuous-time switched systems: A highly maneuverable aircraft technology (HiMAT) vehicle application

This article presents an active fault-tolerant tracking control (FTTC) scheme for switched linear systems with unknown external disturbances and actuator faults. First, a switched adaptive observer (SAO) is designed to simultaneously achieve system state and actuator fault estimation. Second, an active fault-tolerant tracking controller with a reconfigurable adaptive proportional–integral–derivative architecture is proposed based on the results of these estimations. This FTTC technique aims to ensure the tracking of a predefined reference trajectory while also compensating for actuator fault effects. In terms of linear matrix inequalities, less conservatism design conditions for the SAO and fault-tolerant tracking controller are obtained by utilizing the average dwell time technique and multiple Lyapunov functions. Finally, an application to the highly maneuverable aircraft technology vehicle is used to prove the benefits of the presented scheme.

An Advanced Hybrid Model Based On Stochastic - Eulerian Numerical Approach: Application To Atmospheric Pollution

In this paper, we propose for the first time to the best of our knowledge, extend the application of a stochastic Eulerian numerical approach based on the Extended Kalman Filter (EKFE.N.M.) to address the limitations of the Eulerian air pollution model CHIMERE. This approach integrates a comprehensive set of processes, including advection, turbulence, chemical reactions, emissions, and deposition, to model the dynamics of pollutant mass concentration. The EKF technique is employed to transform nonlinear dynamic problems into a succession of locally linearized ones, which are then used to estimate system states and adjust pollutant concentrations based on measured data. This stochastic approach is tested through two scenarios: one without external forces or control terms, and another that incorporates external factors like temperature, wind speed, and nitrogen dioxide as ozone precursors. A comparison of the obtained results with those from the standard CHIMERE model and studies from the literature demonstrates the accuracy and effectiveness of the proposed method.

State estimation of discrete event systems using fuzzy timed petri nets

State estimation of discrete event systems using fuzzy timed petri nets

Multiple-model-based adaptive state fusion estimation of IWMD-EV using SSUKF

Abstract To improve the preciseness degree and adaptive adjustment ability of the state acquisition system under multiple operating conditions, a vehicle state fusion estimation strategy using strong-tracking suboptimal unscented Kalman filtering (SSUKF) algorithm and adaptive weights is proposed. The vehicle models were established by comprehensively characterizing the multi-parameter mapping relationship under the kinematic, dynamic, and electromechanical coupling driving relationship of in-wheel motor drive electric vehicle (IWMD-EV). To improve estimation performance of vehicle state estimation system in face of nonlinear factors such as noise and interference, a vehicle kinematic-based observer (KO) and a dynamic-based observer (DO) were developed based on the SSUKF algorithm. In addition, to enhance the overall preciseness degree and its adaptive adjustment ability for large-scale road conditions, a state fusion estimation method with adaptive weight is presented by combining redundant information of multiple model observers. The results demonstrated that the proposed method can significantly improve the estimation preciseness degree and the adaptive ability for complex working conditions.

Distributed state estimation of interconnected power systems with time‐varying disturbances and random communication link failures

AbstractState estimation of multi‐area interconnected power systems is crucial for reflecting system operations and guiding actuator responses. However, sensor faults, communication link failures, and external random disturbances can inevitably lead to power system failures. Therefore, designing a highly effective state estimation method capable of timely and accurate detection of sensor faults in the power grid to mitigate losses is of significant practical importance. This paper addresses the fault estimation problem in multi‐area power systems with parameter uncertainties and proposes a fault‐tolerant state estimator that accounts for communication link failures between network layers in each area. These communication link failures are modelled as Bernoulli‐distributed variables. State estimation is achieved using information from adjacent power system areas. Sufficient conditions for the error system's performance are provided using Lyapunov stability theory and linear matrix inequality methods. Finally, simulations on a three‐area interconnected power system validate the proposed method's effectiveness in mitigating the effects of communication link failures and random disturbances. The method accurately and rapidly estimates sensor faults and the system state, ensuring stable operation and enhancing grid reliability.

Distributed State Estimation for Linear Systems in Networks With Antagonistic Interactions.

This article deals with the distributed state estimation problem for linear systems in networks with cooperative interactions and antagonistic interactions, where the cooperative interactions and the antagonistic interactions are characterized by the positive weights and the negative weights, respectively. Due to the coexistence of the cooperative interactions and the antagonistic interactions, the existing methods based on the non-negatively weighted graph become not applicable. First, a partition method of the nodes and a decomposition form of the system matrices are introduced. Then a new form of distributed observers is proposed in the network with cooperative interactions and antagonistic interactions. Necessary and sufficient conditions, which guarantee the existence of proposed distributed observers, are presented. In particular, when the communication network is cooperative, the proposed method is suitable for two cases, that is, the nodes in each independent strongly connected component are jointly detectable, or each node is jointly detectable with its neighbors. Finally, three examples are simulated to illustrate the effectiveness of the proposed methods.

Stubborn state estimation for time-delay systems with relay communication network: The half-duplex case

Stubborn state estimation for time-delay systems with relay communication network: The half-duplex case

UKF-Based Optimal Tracking Control for Uncertain Dynamic Systems With Asymmetric Input Constraints.

To enhance system robustness in the face of uncertainty and achieve adaptive optimization of control strategies, a novel algorithm based on the unscented Kalman filter (UKF) is developed. This algorithm addresses the finite-horizon optimal tracking control problem (FHOTCP) for nonlinear discrete-time (DT) systems with uncertainty and asymmetric input constraints. An augmented system is constructed with asymmetric control constraints being considered. The augmented problem is addressed with a DT Hamilton-Jacobi-Bellman equation (DTHJBE). By analyzing convergence with regard to the cost function and control law, the UKF-based iterative adaptive dynamic programming (ADP) algorithm is proposed. This algorithm approximates the solution of the DTHJBE, ensuring that the cost function converges to its optimal value within a bounded range. To execute the UKF-based iterative ADP algorithm, the actor-estimator-critic framework is built, in which the estimator refers to system state estimation through the application of UKF. Ultimately, simulation examples are presented to show the performance of the proposed method.

Learning-based state estimation in distribution systems with limited real-time measurements

The task of state estimation in active distribution systems faces a major challenge due to the integration of different measurements with multiple reporting rates. As a result, distribution systems are essentially unobservable in real time, indicating the existence of multiple states that result in identical values for the available measurements. Certain existing approaches utilize historical data to infer the relationship between real-time available measurements and the state. Other learning-based methods aim to estimate the measurements acquired with a delay, generating pseudo-measurements. Our paper presents a methodology that utilizes the outcome of an underdetermined state estimator of an unobservable network state estimator to exploit information on the joint probability distribution between real-time available measurements and delayed ones to generate new physics-informed interpretable features. Through numerical simulations conducted on two realistic distribution grids of different size with insufficient real-time measurements, the proposed procedure showcases superior performance compared to existing state forecasting approaches and those relying on inferred pseudo-measurements.

Tracking and Fault-Tolerant Controller Design for Uncertain Steer-by-Wire Systems Using Model Predictive Control

This study presents a tracking and fault-tolerant controller architecture for uncertain steer-by-wire (SbW) systems using model predictive control in the presence of actuator malfunction and the nonlinear properties of tire lateral stiffness coefficients. By changing the internal model, the model predictive control (MPC) technique was used to achieve optimal tracking performance under the actuator output limitation variation problem and uncertain system parameters. System parameters and state estimates were simultaneously provided by the fault detection and isolation modules to detect actuator failure using the coupling estimation approach. The estimation accuracy was further improved by considering the replacement errors as virtual noise, which was also estimated during the estimation process. Simulation and experimental results demonstrate that the proposed fault-tolerant control technique can identify motor faults and conduct fault-tolerant control based on fault identification, showing good front-wheel steering angle tracking performance under both normal and fault conditions.

Research on Fast Early Warning of False Data Injection Attack in CPS of Electric Power Communication Network

The power grid is vulnerable to bad data interference and false data attacks, so its security is reduced. This paper focuses on the study of false data injection attacks (FDIAs), analyzes the principle of FDIAs and their impact on power systems, and studies the methods of suppressing and detecting FDIAs based on distributed state estimation and neural networks. In addition, this paper establishes a specific simulation model. Simulation results show that the proposed method can effectively identify FDIAs and correct bad data, thus further reducing the impact of FDIAs on power system state estimation. Therefore, in the follow-up, we can use this method to carry out practical research in the power communication network to further improve the security of the power communication network.