State Estimation Error Research Articles

Observer-Based, Robust Position Tracking in Two-Mass Drive System

Precise motion control remains one of the most important problems in modern technology. It is especially difficult in the case of two-mass systems with flexible coupling if only the motor position and velocity are measured. We propose a new methodology of control system design in this situation. The concept is founded on a robust observer design, based on a linear matrix inequality (LMI) solution. The observer cooperates with the original nonlinear controller. The presented approach allows us to solve the position tracking problem for a two-mass drive, with unknown parameters, in the presence of disturbances (for instance, nonlinear friction-like torques) acting on both ends of the flexible shaft. Under this set of assumptions, the problem was never solved previously. The closed-loop system stability is investigated, and the uniform ultimate boundedness of state estimation errors and tracking errors is proven using Lyapunov techniques. Numerical properties of the design procedure and characteristic features of the observer, controller, and closed-loop system are demonstrated by several examples.

An approximate minimum mean-square error estimator for linear discrete time-varying systems: Handling Try-Once-Discard protocol

This paper is concerned with the remote state estimation problem for a class of linear discrete time-varying stochastic systems under communication constraints. In order to mitigate the undesired phenomena of data collisions, a Try-Once-Discard (TOD) protocol is utilized to regulate the signal transmissions over the sensor-to-estimator communication channel, where the TOD protocol is based on the scheduling rule described by a specific switching function. Under the introduced TOD protocol, the approximate minimum mean-square error (MMSE) state estimation problem is investigated and a recursive algorithm is developed for the MMSE estimator design whose computational complexity is comparable to that of the conventional Kalman filter. Furthermore, some conditions are established for the boundedness of the estimation error covariance. A numerical example is presented to illustrate the effectiveness of the proposed MMSE estimator.

False Phasor Data Detection Under Time Synchronization Attacks: A Neural Network Approach

Phasor measurement units (PMUs) used in the smart grids are vulnerable to time synchronization attacks (TSA), whose attack target is the global positioning systems (GPS). The attacker manipulates phase measurements by sending deceptive GPS signals to introduce errors in state estimation, which can affect bus power flow calculation and economic dispatching of the power system. Considering the case of multiple attacked PMUs in AC, a novel false phase data detection method is proposed in this paper. The method uses “phase coding” to extract and encode the potential relationship between amplitude and phase angle, and then builds a TSAs detection model based on a vector neural network that learns the encoded relationship vectors through dynamic routing. Finally, simulation experiments are carried out on IEEE 9, 14, 30, and 118 bus systems and real measurements provided by a province in China. The results show that the proposed method achieves the best performance among the detection methods based on the learning model.

Secure Distributed Adaptive Platooning Control of Automated Vehicles Over Vehicular Ad-Hoc Networks Under Denial-of-Service Attacks.

This article deals with the problem of secure distributed adaptive platooning control of automated vehicles over vehicular ad-hoc networks (VANETs) in the presence of intermittent denial-of-service (DoS) attacks. The platoon, which is wirelessly connected via directed vehicle-to-vehicle (V2V) communication, is composed of a group of following vehicles subject to unknown heterogeneous nonlinearities and external disturbance inputs, and a leading vehicle subject to unknown nonlinearity and external disturbance as well as an unknown control input. Under such a platoon setting, this article aims to accomplish secure distributed platoon formation tracking with the desired longitudinal spacing and the same velocities and accelerations guided by the leader regardless of the simultaneous presence of nonlinearities, uncertainties, and DoS attacks. First, a new logical data packet processor is developed on each vehicle to identify the intermittent DoS attacks via verifying the time-stamps of the received data packets. Then, a scalable distributed neural-network-based adaptive control design approach is proposed to achieve secure platooning control. It is proved that under the established design procedure, the vehicle state estimation errors and platoon tracking errors can be regulated to reside in small neighborhoods around zero. Finally, comparative simulation studies are provided to substantiate the effectiveness and merits of the proposed control design approach on maintaining the desired platooning performance and attack tolerance.

A Novel Federated Structure of Invariant EKF Using Left-/Right-Invariant Observations

In this article, we propose a novel federated structure of the invariant extended Kalman filter (IEKF) using the left- and right-invariant observations. A proper invariant error should be chosen to exploit the trajectory-independent property of the IEKF. For the left- and right-invariant observations, the left-IEKF (LIEKF) and the right-IEKF (RIEKF) are designed, respectively. However, in applications, both left- and right-invariant observations are often used together while using multiple aiding sensors to improve estimation performance. If either the LIEKF or RIEKF is selected and implemented as a centralized filter, the measurement matrix contains current state estimates in mismatched observation-related terms. As a result, as the state estimation error increases, the calculation of the Kalman gain is affected, and the filter cannot properly correct the error. For such situations, we propose a federated structure that updates the left- and right-invariant observations separately in the allocated subfilters. In the subfilter assigned with left-invariant observations, the error is corrected using the LIEKF, and in the subfilter assigned with right-invariant observations, the error is corrected using the RIEKF. Since each subfilter uses trajectory-independent Kalman gain, it is expected to improve the estimation performance compared to the centralized structure. The performance of the proposed method is evaluated and compared to the centralized LIEKF and RIEKF through Monte-Carlo simulations for an inertial navigation example. Also, the proposed method is validated by a publicly available dataset of a ground vehicle equipped with a global positioning system (GPS) and wheel encoders.

Design of delay-dependent state estimation algorithm for nonlinear coupling complex networks with dynamical bias: An adaptive event-triggered scheme

This paper is concerned with the delay-dependent variance-constrained state estimation (DDVCSE) problem for nonlinear coupling complex networks (NCCNs) subject to dynamical bias and adaptive event-triggered mechanism (AETM). First of all, the nonlinear coupling is modeled to embody the form of data exchange between different network units, which is linearized by resorting to the Taylor expansion. Then, an augmented technique is adopted to deal with the random bias described by a dynamical equation. Furthermore, an AETM is arranged in the sensor-to-estimator channel to adjust communication rate thereby averting resource waste. A novel augmented delay-dependent state estimator is constructed such that the upper bound of state estimation error covariance (UBSEEC) can be derived in the presence of state delay, nonlinear coupling, dynamical bias and AETM. Moreover, the estimator gain is designed appropriately in the sense of locally minimized variance-constrained index. Besides, the algorithm performance issue is discussed with rigourous mathematical proof, where the monotonicity of the trace of UBSEEC with respect to coupling strength is clarified in detail. Finally, an illustrative example is carried out to demonstrate the validity of the developed DDVCSE strategy.

Observer-based adaptive ISMC for connected vehicles against cyber-attacks

This paper concentrates on decentralized variable structure adaptive integral sliding mode control (ISMC) for connected vehicles (CV) against cyber-attacks. First of all, a novel vehicle leader-follower model is established by jointly considering the cyber-attacks which involve replay attack and DoS attack simultaneously. Secondly, a decentralized control scheme is designed on the basis of the variable structure observer and adaptive integral sliding mode technique. The Lyapunov-Razumikhin method is adopted such that the state estimation error of CV system is asymptotically converged to zero, which can overcome the replay attack, DoS attack, and measurement delays, then a corrective signal is designed for the deception attack to eliminate the influence of deception attack on the CV system. Furthermore, the robust asymptotic stability of CV system is guaranteed by exploiting the emerging technique of robust control for time-delay systems. Meanwhile, the string stability of CV is guaranteed, even under the condition of heterogeneous vehicles. Finally, extensive simulations are conducted to verify the theoretical analysis and demonstrate the effectiveness and superiority of the proposed method.

Minimum‐variance recursive state estimation for complex networks with stochastic switching topologies and random quantization under try‐once‐discard protocol

SummaryThis article is concerned with the issue of minimum‐variance recursive state estimation (MVRSE) for a class of nonlinear dynamical complex networks (NDCNs) with stochastic switching topologies and random quantization under the try‐once‐discard (TOD) protocol. Two sequences of Bernoulli distributed random variables with given occurrence probabilities are utilized to characterize the stochastic switching manners of network topologies and the randomly occurring quantized output measurements, where the quantization effects are portrayed by the uniform quantizer. Moreover, the TOD protocol is adopted to arrange the order of the information transmission of network nodes so as to alleviate the communication burden and mitigate the network congestions. The focus of the MVRSE issue is to develop a novel state estimation algorithm such that, for all stochastic switching topologies, random quantization effects and TOD protocol, an optimized upper bound of the estimation error covariance is guaranteed by properly designing the estimator gain. In addition, the theoretical proof is derived, which illustrates that the state estimation error is exponentially mean‐square bounded under certain conditions. Meanwhile, we also present the related theoretical analysis, which discusses the impact caused by random quantization. Finally, a numerical experiment is utilized to show the validity of the novel MVRSE approach.

Finite‐time secure state estimation for a class of switched systems subject to deception attacks

AbstractThis article is concerned with the finite‐time secure state estimation problem for switched systems subject to malicious attacks. The sensor data is considered transmissible via a non‐secure communication network environment, where the communication channel might be subject to deception attacks. By dividing the sensor data that is subject to attacks into two parts, related and unrelated to the original measurements, a switched secure state estimation error system model is established. Moreover, based on the average dwell time method, sufficient conditions are derived for the switched secure state estimation error system to be finite‐time stable, as well as finite‐time boundedness. An existence condition of the finite‐time secure state estimator gains with a desired performance is given. Subsequently, the finite‐time secure state estimator gains' design is transformed to solve a set of linear matrix inequalities. Finally, numerical examples are used in order to show the effectiveness of the proposed finite‐time secure state estimator design method.

Robust fault estimation for polynomial systems with time delay via a polynomial adaptive observer

In this paper, a robust fault estimation for polynomial systems with time delay via a polynomial adaptive observer is presented and described. In fact, in contrast to previous research works on actuator faults, the learning rate utilized to govern the convergence speed of states and faults errors is not predetermined but is derived using the sum of squares optimization problem. Furthermore, the [Formula: see text] optimization approach was created to reduce the impact of disturbances on state estimation error and fault estimation error. Finally, an illustrative practical example is given to validate the effectiveness of the suggested methodology.

Stealthy switching attacks on sensors against state estimation in cyber‐physical systems

AbstractThis article focuses on designing sensor attacks to deteriorate the state estimation in cyber‐physical systems. The scenario that the malicious attack signals can be injected into different but limited number of sensor communication channels is considered. The state estimation error variations and innovation variations are adopted to measure attack performance and attack stealthiness, respectively. A switching attack strategy is proposed, under which the estimation error variations are driven to the predesigned target value and the norm of innovation variations remains at a small level. The switching attack design problem is formulated as a discrete switched optimal control problem which can be solved by dynamic programming, while the computational burden is heavy. To overcome this difficulty, by using pruning technique to remove the redundant matrices generated in dynamic programming, the quadratic optimization problem becomes numerically tractable. In this way, the suboptimal attack signal sequence and switching sequence can be acquired. Finally, a simulation example is provided to illustrate the effectiveness of the proposed attack strategy.

Improved adaptively robust estimation algorithm for GNSS spoofer considering continuous observation error

Once the spoofer has controlled the navigation system of unmanned aerial vehicle (UAV), it is hard to effectively control the error convergence to meet the threshold condition only by adjusting parameters of estimation if estimation of the spoofer on UAV has continuous observation error. Aiming at this problem, the influence of the spoofer's state estimation error on spoofing effect and error convergence conditions is theoretically analyzed, and an improved adaptively robust estimation algorithm suitable for steady-state linear quadratic estimator is proposed. It enables the spoofer's estimator to reliably estimate UAV status in real time, improves the robustness of the estimator in responding to observation errors, and accelerates the convergence time of error control. Simulation experiments show that the mean value of normalized innovation squared (NIS) is reduced by 88.5%, and the convergence time of NIS value is reduced by 76.3%, the convergence time of true trajectory error of UAV is reduced by 42.3%, the convergence time of estimated trajectory error of UAV is reduced by 67.4%, the convergence time of estimated trajectory error of the spoofer is reduced by 33.7%, and the convergence time of broadcast trajectory error of the spoofer is reduced by 54.8% when the improved algorithm is used. The improved algorithm can make UAV deviate from preset trajectory to spoofing trajectory more effectively and more subtly.

Collaboration of Heterogeneous Marine Robots Toward Multidomain Sensing and Situational Awareness on Partially Submerged Targets

This article reports on a multirobot system that collaboratively obtains above-water, surface, and below-water information on a floating target. This capability allows a ship to autonomously survey and obtain situational awareness on a floating unresponsive target from a safe stand-off before inspecting it more closely or navigating around it. The target could be another ship, structure, or a navigational obstruction like an iceberg. The proposed solution is a collaborative system with an unmanned aerial vehicle (UAV), an unmanned underwater vehicle (UUV), and an unmanned surface vehicle (USV). The UAV captures visual imagery to create a 3-D model of the target’s above-water geometry using photogrammetry. The UUV surveys the target’s submerged hull with integrated imaging and profiling bathymetric sonars. The USV hosts an intelligent mission-planning node which manages the robotic collaboration in a centralized architecture by autonomously planning and distributing the missions for the UUV and UAV. The intelligent node also adaptively plans the USV’s trajectory to support the other autonomous assets, specifically reducing and bounding the UUV’s state-estimate error through collaborative localization. The resulting above- and below-water sensor data is fused at the waterplane, using a sliding correlation algorithm, to yield a 3-D representation of the floating unresponsive target. The contributions from this article include the cross-domain robotic collaboration and autonomous mission-planning toward acquiring and fusing data from heterogeneous robots. The autonomous mission-planning and data-merging algorithms are presented. The setup and results from simulations and in-water testing with an UUV, USV, and UAV are described.

Joint Beamforming Design for IRS Aided Multiuser MIMO With Imperfect CSI

This paper investigates the joint beamforming design for the intelligent reflecting surface (IRS) aided multi-antenna multiuser (MU) multiple-input multiple-output (MIMO) downlink transmissions under imperfect channel state information (CSI), where the IRS can only take discrete PSs (PSs) at each element and the weighted sum rate (WSR) is adopted as the performance metric. By deriving the covariance matrix of the interference and noise at the users under the statistical channel estimation errors (CEEs) model, the joint WSR maximization problem is reformulated as an equivalent weighted minimum mean square error minimization problem and decoupled into two subproblems which are solved alternatively. In particular, two algorithms based on the majorization-minimization and gradient descent methods are proposed to obtain the optimal beamforming matrix at the IRS. Simulation results validate the accuracy of the proposed robust design and reveal that in case of imperfect CSI, the IRS can still achieve a significant improvement in WSR even with 2-bits PSs at the IRS. Moreover, it is also found that increasing the number of reflecting elements may not always be beneficial and that the optimal location of the IRS may be closer to the base station in the presence of CEEs.

Adaptive Event-Triggered Transmission Scheduling in Rate-Limited Multiloop Remote Control

This article studies the dynamic transmission-scheduling problem of rate-limited networked control systems with multiple loops. It is critical to develop an optimal-scheduling policy because, due to limited spectrum resources and energy budgets, only partial subsystems may have access to shared channels at each time step to update the plant states affected by stochastic disturbances. An adaptive event-triggered stochastic scheduling policy is proposed based on the one-step-ahead comparison error of state estimation between the sensor and controller. By formulating the scheduling problem as a constrained multiagent partially observable Markov decision process, a multiagent reinforcement learning algorithm is proposed to search for the optimal parameters of the scheduling policy. And an edge-assisted learning architecture is introduced to facilitate its implementation. An explicit performance index of the optimal scheduling is further obtained, revealing the effects of system disturbances, observation noises, and the communication rate constraint. Moreover, two numerical examples are given to validate the proposed scheduling policy, showing that it outperforms several competitive scheduling schemes. Due to the low computational complexity, the proposed scheduling may have an advantage in large-scale heterogeneous control systems, e.g., the flow and pressure control in fluid transport pipelines.

Positive observers for semilinear positive systems

Abstract The problem of designing a positive Luenberger observer for a class of infinite-dimensional semilinear positive systems is addressed. The proposed observer is positive. That is, it ensures that the state estimates are non-negative at any time. The positive observer is designed based on positive bounded perturbation results. In particular it is shown that, under suitable conditions the state estimation error converges exponentially to zero. The results are illustrated by numerical simulations based on an exothermic Plug-Flow Tubular reactor model and show the effectiveness of the proposed positive observer.

Optimal placement of distribution-level synchrophasor sensors for distribution system

This paper proposes a new method for the placement of the important synchrophasor sensors, the distribution-level phasor measurement units (DPMUs). A new objective function is developed to achieve minimization of distribution system state estimation errors where the limited number of DPMUs, the zero injection buses, the limited DPMU channels and the supervisory control and data acquisition measurements are taken into account. The A-optimal experimental design criterion is used to formulate the proposed objective function and constraints. The state estimates are obtained by using the maximum likelihood estimator where both Gaussian and non-Gaussian measurement noise scenarios are studied. The performance of the proposed method is demonstrated by simulations on IEEE 34-bus and 123-bus distribution systems.

Maneuvering Extended Object Tracking with Modified Star-Convex Random Hypersurface Model Based on Minimum Cosine Distance

Maneuvering extended object tracking is a new research field due to the rapid development of modern sensor technology. Multiple measurements may be resolved from different unknown sources on an object by using a high-resolution radar. In this case, the object should be regarded as an extended one with object extension, e.g., its shape may be described by the star-convex random hypersurface model. This model is usually specified by a one-dimensional radial function. However, the divergence of the shape estimation and a high error of the kinematic state estimation are likely to occur when an extended object maneuvers. This is because the radial function may take a negative value after Fourier series expansion, which leads to unpredictable estimation results. Unfortunately, the model itself is unable to solve this problem via the subsequent iterations. In this paper, we proposed a modified shape estimation approach to track an extended object with a star-convex random hypersurface model based on minimum cosine distance. Both the extension state and kinematic state at the current time are reinitialized once the radial function takes a negative value. Moreover, a mathematical model was constructed by using the principle of minimum cosine distance, so as to obtain more reasonable weight distribution coefficients for the correction of the extension state. Simulation results in different scenarios demonstrated the effectiveness of the proposed tracking approach.

Adaptive fast desensitized ensemble Kalman filter for uncertain systems

The classical desensitized ensemble Kalman filter can effectively tolerate uncertain parameters of the system. However, the method of solving the gain matrix by algebraic equations must be solved, and the sensitivity-weight must be adjusted in real-time during the filtering process. An adaptive fast desensitized ensemble Kalman filter (AFDEnKF) is proposed to reduce computational cost and adaptively adjust the sensitivity-weight in real-time. In case of the AFDEnKF, an analytical gain matrix is obtained by desensitizing the sensitivity of the state estimation error to the uncertain parameters and minimizing cost functions, and an adaptive factor is introduced to adjust automatically sensitivity-weight by using the orthogonal principle of measurement residuals. Three numerical examples are employed to demonstrate the effectiveness of the proposed AFDEnKF. The simulation results show that the AFDEnKF can effectively improve the computational efficiency and the state estimation accuracy.

Neural network-based control for RRP-based networked systems under DoS attacks with power interval

This paper is concerned with the optimal control problem for networked systems with the round-robin protocol (RRP) under the denial-of-service (DoS) attacker with power interval. In the literature, the control design is studied for the linear networked system subject to the DoS attacks with a known constant power or a known constant probability of data-packet dropouts. In this paper, the objective is to control the unknown nonlinear system in the communication network subject to the DoS attacks with a power interval and a time-varying probability of data-packet dropouts. The effects of the DoS attacks with power interval on a networked system under RRP are modeled accurately. A neural network (NN) -based observer is designed for the nonlinear system under the DoS attacks with power interval, and the relationship between the DoS attacker power interval and state estimation error is obtained. The NN actor–critic policy for the optimal control of the RRP-based networked system under the DoS attacks with power interval is found with adaptive dynamical programming, and stability of the resulting control system is analyzed. The proposed control method is demonstrated by a networked uninterruptible power supply system.