State Estimation Error Research Articles

Observer based attack detection and security control for UAVs against attacks on desired trajectory

This paper investigates an attack detection and security control strategy for unmanned aerial vehicles (UAVs) in the presence of malicious attacks. The detection, estimation, and compensation of the attack are the key points of the proposed scheme. This article considers that the desired trajectory sent by the ground control station (GCS) to the UAV is maliciously tampered with. First, a description of the UAV system and the desired trajectory attack is presented. The mathematical model is constructed by analyzing the characteristics of the desired trajectory attack. Secondly, an unknown input observer (UIO) is designed to generate the state estimation error. The attack detection framework is constructed by taking into account the state estimation error and the trajectory tracking error. Thirdly, an attack estimation observer with a prescribed H∞ performance is designed to compensate for the impact of attacks on the control system. A disturbance observer (DO) is used to compensate for the system disturbance. Finally, the simulation results are presented on Matlab and Gazebo to validate the effectiveness of the proposed security control strategy.

Probability‐guaranteed encoding–decoding‐based state estimation for delayed memristive neutral networks with event‐triggered mechanism

SummaryThis article handles the probability‐guaranteed state estimation problem for a class of nonlinear memristive neural networks (MNNs) by using an event‐triggered mechanism. Both time‐varying delays and incomplete measurements are considered in the MNNs dynamics. To mitigate the impact of limited communication bandwidth, a communication protocol is proposed that incorporates an encoding–decoding technique in addition to an event‐triggered scheme. The aim is to devise a state estimator that can estimate the states of MNNs, ensuring that the state estimation error falls within the required ellipsoidal area with a desired chance. We obtain sufficient conditions for the feasibility of the addressed problem, where the requested gains can be found iteratively by solving certain convex optimization problems. On the basis of the proposed framework, some issues are further presented to determine locally optimal estimator parameters according to different specifications. Finally, we utilize an illustrative numerical example to show the validity of our provided theoretical results.

Learning-Based Vehicle State Estimation Using Gaussian Process Regression Combined with Extended Kalman Filter

In order to address the challenge of accurate vehicle state estimation, especially in highly nonlinear and complex operating conditions, this paper proposes a learning-based method for vehicle state estimation. To achieve this, a novel theoretical framework is constructed that combines the model-based Extended Kalman Filter (EKF) with Gaussian process regression (GPR). By establishing a dynamic model of the vehicle and describing the errors using machine learning techniques, the sources of state estimation errors are analyzed. Furthermore, by considering the model uncertainty, an error prediction model is developed through GPR learning from real-world vehicle data. Combined with EKF, the proposed method enables high-precision online estimation of vehicle state. To validate the proposed method, tests are performed on a real vehicle test platform equipped with high-precision sensors and data acquisition equipment, under two different operating conditions: emergency and normal. The results are compared with those obtained using EKF and State Observer, which demonstrates a more accurate and adaptable vehicle state estimation, and provides a method for quantitatively describing the confidence interval of vehicle state estimation result.

IoT and machine learning approach for the determination of optimal freshwater replenishment rate in aquaponics system

IoT and machine learning approach for the determination of optimal freshwater replenishment rate in aquaponics system

Output feedback control for hypersonic flight vehicles via distributed high-gain observer

During the hypersonic flight process of rigid hypersonic flight vehicles (HFVs), the flight-path angle and angle of attack are usually small and sensitive to flight condition variation, the accurate measurements are difficult, subsequently the formulation of states observers is an urgent issue. A distributed high-gain observer is proposed to reconstruct the admissible system state dynamics based on limited measured output. First, a distributed observer is proposed for the cascade strict-feedback system to ensure the global convergence of the state estimation errors between the estimated state in each local observer and system states, for the prescribed system initial values. Second, the distributed high-gain observer-based nonlinear control is investigated on the longitudinal dynamics of HFVs with partial measurable states. The rigid body system dynamic is divided into the altitude subsystem and the velocity subsystem. In the altitude subsystem, the proposed distributed high-gain observer is formulated to exact estimate the flight-path angle and angle of attack, and then the back-stepping design is proposed for constructing the controllers. The nonlinear dynamic inversion controller is introduced to accomplish the velocity tracking. Finally, simulation examples are served to verify that the proposed output feedback control possesses the superior properties of high tracking performance, fast convergence of state estimation error and easy-implementation.

Supervisory adaptive safety control for uncertain nonlinear systems

This paper investigates the supervisory adaptive safety control problem for uncertain nonlinear systems with unmeasurable states. In order to estimate unknown parameters and unmeasurable states, a supervisory observer framework consisting of a multi-observer bank and a supervisor unit, is proposed based on a dividing rectangles (DIRECT) algorithm. Under a desired accuracy, the parameter estimates converge to near the true parameters within finite-time while the estimation error of the system state converges to a small neighborhood near the origin. Also, an observer robust adaptive control barrier function is constructed to ensure safety for uncertain nonlinear systems by guaranteeing controlled invariance of a time-varying auxiliary set. By adjusting some parameters in the DIRECT algorithm, the time-varying auxiliary set approaches the original safe set, which reduces the conservatism generated by the compression of the safe set. Finally, two examples, including an adaptive cruise control system, are given to demonstrate the effectiveness of the proposed method.

Photovoltaic Hosting Capacity Margin due to State Estimation Error

Photovoltaic Hosting Capacity Margin due to State Estimation Error

Back-and-forth nudging moving horizon estimation for discrete-time linear systems

In this paper, we propose a novel moving horizon estimation algorithm for discrete-time linear systems with a limited number of measurements. Motivated by the idea of the back-and-forth nudging algorithm, we design the back-and-forth nudging in time moving-horizon estimation method by deploying two moving horizon estimators that move backward and forward iteratively. Based on a finite number of measurements, the proposed algorithm can be used for moving-horizon state estimation with guaranteed convergence. By using the proposed method, we show that the norm of the state estimation error is upper bounded by a sequence that converges to its steady-state in finite-time (i.e., using a finite number of measurements), provided that suitable parameters are selected. The unbiasedness properties and comparison results with the conventional (forward-in-time) moving horizon estimation are discussed. The effectiveness of the proposed approach is validated through a numerical example.

A robust state estimation method for power systems using generalized correntropy loss function

The accurate estimation of power system states is crucial for effective monitoring and control. However, the performance of conventional state estimators, which assume Gaussian measurement noise and do not account for denial-of-service attacks, can deteriorate significantly in real power systems. To address these issues, this paper proposes a novel robust state estimation method based on the quadratic function (QF) and the generalized correntropy loss function (GCL). The proposed QF-GCL state estimation method can effectively deal with non-Gaussian measurement noise and denial-of-service attacks. To enhance the computational efficiency, an influence function based solving method is developed. To determine the optimal parameters for the proposed QF-GCL state estimation method, a new state estimation error covariance equation is further derived. Simulations are performed on the IEEE 30-bus, 118-bus and 300-bus systems, to demonstrate the accurate and robust performance of the proposed QF-GCL robust state estimation method.

Learning Dynamic Compact Memory Embedding for Deformable Visual Object Tracking.

Recently, template-based trackers have become the leading tracking algorithms with promising performance in terms of efficiency and accuracy. However, the correlation operation between query feature and the given template only achieves accurate target localization, but is prone to state estimation error, especially when the target suffers from severe deformation. To address this issue, segmentation-based trackers are proposed that use per-pixel matching to improve the tracking performance of deformable objects effectively. However, most of the existing trackers only match with the target features of the initial frame, thereby lacking the discrimination for handling a variety of challenging factors, e.g., similar distractors, background clutter, and appearance change. To this end, we propose a dynamic compact memory embedding technique to enhance the discrimination of the segmentation-based visual tracking method that can well tell the target from the background. Specifically, we initialize a memory embedding with the target features in the first frame. During the tracking process, the current target features that have certain correlation with the existing memory are updated to the memory embedding online. To further improve the tracking accuracy for deformable objects, we use a weighted point-to-global matching strategy to measure the correlation between the pixelwise query feature and the whole template, so as to capture more detailed deformation information. Extensive evaluations on six challenging tracking benchmarks including VOT2016, VOT2018, VOT2019, GOT-10K, TrackingNet, and LaSOT demonstrate the superiority of our method over recent remarkable trackers. Besides, our tracker outperforms the excellent segmentation-based trackers, i.e., D3S and SiamMask on the DAVIS2017 benchmark. The code is available at https://github.com/peace-love243/CMEDFL.

A new H∞ observer for continuous LPV systems with unknown inputs using an HOSM differentiator

Abstract The main contribution of this paper is the development of $H_{\infty }$ state and unknown input (UI) observers for noisy linear parameter-varying (LPV) systems. The observers are constructed in order to be unbiased (in particular the state estimation error is decoupled from the UI) and with a minimum $L_{2}$ transfer between the perturbations (that are assumed to be with finite energy) and the estimation errors. Contrary to equivalent observers developed in the literature, the present one relaxes a widely used rank condition on the system matrices for decoupling the UI. In order to do so, high-order derivation is needed, which is done using a high-order sliding modes differentiator. A method is given to design observer gains for LPV systems under polytopic form. Finally, three examples illustrate some aspects of the theoretical contributions, and compare this work to the existing ones.

A fractional order model of auxiliary power batteries suitable for hydrogen fuel cell hybrid systems heavy-duty trucks

Aiming at the problem that the existing battery fractional order model is not suitable for the auxiliary power battery of hydrogen fuel cell heavy-duty trucks, considering the characteristics of multiple influencing factors and nonlinearity in actual driving processes, a fractional order model of auxiliary power batteries is proposed based on the hydrogen fuel cell heavy-duty trucks model and the batteries' fractional order model. Then, to solve the charge state estimation error increases due to the high frequency and large rate charging and discharging, H∞ filter is introduced into the adaptive unscented Kalman filter to optimize the charge state estimation in the model. Additionally, the model's parameters are identified using the evolutionary algorithm and the recursive least squares technique based on the forgetting factor. Finally, the model is verified by dynamic conditions. The results show that compared with the auxiliary power batteries' fractional order model, the optimized model reduces the MAE by 0.08% and the RMSE by 0.22% when estimating voltage, and reduces the MAE by 0.25% and the RMSE by 2.66% when estimating SOC. Therefore, the optimized fractional order model of auxiliary power battery has higher accuracy and applicability.

High-Precision Position Tracking Control with a Hysteresis Observer Based on the Bouc–Wen Model for Smart Material-Actuated Systems

The Bouc–Wen model has been widely adopted to describe hysteresis nonlinearity in many smart material-actuated systems, such as piezoelectric actuators, shape memory alloy actuators, and magnetorheological dampers. For effective control design, it is of interest to estimate the hysteresis state that is not measurable. In this paper, the design of a state observer for the Bouc–Wen model is presented. It is shown that, with sufficiently high observer gains, the state estimate error, including that for the hysteresis state, converges to zero exponentially fast. The utility of the proposed hysteresis observer is illustrated in the design of a high precision output-feedback position tracking controller, and the resulting tracking error is shown to decay exponentially via Lyapunov analysis. Simulation and experimental results show that the proposed hysteresis observer and the high precision position tracking controller outperform a traditional extended state observer and the corresponding tracking controller, respectively.

Yaw Stability Control of Unmanned Emergency Supplies Transportation Vehicle Considering Two-Layer Model Predictive Control

The transportation of emergency supplies is characterized by real-time, urgent, and non-contact, which constitute the basic guarantee for emergency rescue and disposal. To improve the yaw stability of the four-wheel-drive unmanned emergency supplies transportation vehicle (ESTV) during operation, a two-layer model predictive controller (MPC) method based on a Kalman filter is proposed in this paper. Firstly, the dynamics model of the ESTV is established. Secondly, the improved Sage–Husa adaptive extended Kalman filter (SHAEKF) is used to decrease the impact of noise on the ESTV system. Thirdly, a two-layer MPC is designed for the yaw stability control of the ESTV. The upper-layer controller solves the yaw moment and the front wheel steering angle of the ESTV. The lower-layer controller optimizes the torque distribution of the four tires of the ESTV to ensure the self-stabilization of the ESTV operation. Finally, analysis and verification are carried out. The simulation results have verified that the improved SHAEKF can decrease the state estimation error by more than 78% and achieve the noise reduction of the ESTV state. Under extreme conditions of high velocity and low adhesion, the average relative error is within 6.77%. The proposed control method can effectively prevent the instability of the ESTV and maintain good yaw stability.

Learning-Based Faulty State Estimation Using SOH-Coupled Model Under Internal Thermal Faults in Lithium-Ion Batteries

Estimating the state of charge (SOC), state of health (SOH), and core temperature under internal faults will significantly improve the battery management system’s (BMS’s) autonomy and accuracy in range prediction. This paper presents a neural network (NN) based state estimation scheme that can estimate the SOC, core temperature, and SOH under internal faults in lithium-ion batteries (LIBs). First, we propose a model-based internal fault detection scheme by employing a SOH-coupled electro-thermal-aging model (ETA) of the LIB. Then, a nonlinear observer is used to estimate the proposed SOH-coupled model’s healthy states for a residual generation. The fault diagnosis scheme compares the output voltage and surface temperature residuals against the designed adaptive threshold to detect thermal faults. The adaptive threshold effectively alleviates the false positives due to degradation and model uncertainties of the battery under no-fault conditions. Upon fault detection, we employ an additional NN-based observer in the second step to learn the faulty dynamics. A novel NN weight tuning algorithm is proposed using the measured voltage, surface temperature, and estimated healthy states. The convergence of the nonlinear and NN-based observer state estimation errors is proven using the Lyapunov theory. Finally, numerical simulation results are presented.

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

This work addresses design of an adaptive controller for nonlinear fractional‐order (FO) systems in the strict‐feedback form. The system is subject to unknown dynamics, unavailable state variables, quantized input and output, and input nonlinearity. The fuzzy logic system (FLS) is used to estimate the unknown dynamics, and instead of updating all the regressor weights, only the maximum of their norms is updated, which significantly reduces the computational load. Limitations imposed by data transmission bandwidth have been addressed by incorporating sector‐bounded quantizers, which include both logarithmic and hysteresis quantizers at the system input and output, and their errors have been considered in the controller design. It is assumed that system states are not measured. To estimate the system states, a linear observer has been used. Because of output quantization, the continuous output signal is not available, and therefore the observer has been designed based on the quantized output signal. In addition, the constraints of input nonlinearities, including symmetric and asymmetric saturation, backlash, hysteresis, and dead‐zone, have been considered in the controller design. Input nonlinearity and input quantization have been investigated simultaneously, which makes the analysis more challenging. Moreover, it is assumed that the type of input nonlinearity and its characteristics are not known, which makes the controller design more difficult. These problems have been resolved by using two novel adaptive laws. The adaptive backstepping method and the direct Lyapunov stability analysis have been used to construct the controller, and a nonlinear modified FO filter is used to avoid the explosion of complexity occurring in the traditional backstepping technique. Stability of the closed loop system has been established, and it has been shown that the tracking and state estimation errors converge to a small neighborhood of the origin. Finally, the proposed controller performance has been demonstrated via three simulation examples.

Reinforcement learning‐based event‐triggered optimal control for unknown nonlinear systems with input delay

AbstractThe optimal control issue of discrete‐time nonlinear unknown systems with time‐delay control input is the focus of this work. In order to reduce communication costs, a reinforcement learning‐based event‐triggered controller is proposed. By applying the proposed control method, closed‐loop system's asymptotic stability is demonstrated, and a maximum upper bound for the infinite‐horizon performance index can be calculated beforehand. The event‐triggered condition requires the next time state information. In an effort to forecast the next state and achieve optimal control, three neural networks (NNs) are introduced and used to approximate system state, value function, and optimal control. Additionally, a M NN is utilized to cope with the time‐delay term of control input. Moreover, taking the estimation errors of NNs into account, the uniformly ultimately boundedness of state and NNs weight estimation errors can be guaranteed. Ultimately, the validity of proposed approach is illustrated by simulations.

Finite‐dimensional, output‐predictor‐based, adaptive observer for heat PDEs with sensor delay

SummaryWe are considering the problem of designing observers for heat partial differential equations (PDEs) that are subject to sensor delay and parameter uncertainty. In order to get finite‐dimensional observers, described by ordinary differential equations (ODE), we develop a design method based on the modal decomposition approach. The approach is extended so that both parameter uncertainty and sensor delay effects are compensated for. To cope more effectively with sensor delay, an output predictor is designed and the online provided output predictions are substituted to the future output values in the observer. To compensate for parameter uncertainty, we design a parameter estimator providing online parameter estimates, which are substituted to the unknown parameters in the observer. The parameter estimator design is made decoupled from the observer gain design by using an appropriate decoupling transformation. Using an analysis of the small‐gain‐theorem type, the whole (state and parameter) estimation error system is shown to be exponentially stable, under well‐defined conditions on the observer dimension, the sensor delay, and signal persistent excitation (PE).

Sensor Fault Detection and Diagnosis of Linear Parabolic PDE Systems With Unknown Inputs

This paper investigates the sensor bias fault detection and diagnosis problem for linear parabolic partial differential equation (PDE) systems under the existence of unknown input signals. A variation of Wirtinger's inequality is used to design a Luenberger-type PDE observer and radial basis function (RBF) neural networks are applied to approximate the unknown inputs, guaranteeing the boundedness of the state estimation error. Taking the measurement error as the fault indication signal, a residual evaluation logic is developed to achieve fault detection. An adaptive diagnostic law is constructed to estimate the values of sensor bias faults once they are detected. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula> -modification RBF neural networks are designed to compensate for the unknown inputs in the presence of sensor faults, ensuring that both state and sensor bias faults estimation errors converge to some adjustable sets. The effectiveness and applicability of the developed fault diagnosis strategy are demonstrated by simulation results on a heat diffusion process.

Optimal design of Luenberger reduced-order observer with low sensitivity for linear multivariable systems

For the linear multivariable systems, by combining both merits of orthogonal-function approach and evolutionary optimization, in this paper, a new method is presented for designing a Luenberger reduced-order observer to solve the low-sensitivity design issue for physical system parameter deviation and simultaneously to minimize a measurement of the quadratic performance for reducing state transient estimation error. Two given examples illustrate the effectiveness of the presented new low-sensitivity design approach on state estimation performance. From the given examples, it shows that the estimated state errors are not sensitive to system parameter deviation and have the asymptotical convergence property. Besides, the performances are apparently superior to those without considering low-sensitivity design means.