State Estimation Of Nonlinear Systems Research Articles

State estimation for nonlinear systems using a recurrent neural network learning algorithm and an event-triggered state observer

State estimation for nonlinear systems using a recurrent neural network learning algorithm and an event-triggered state observer

Improved Particle Filter Algorithm for Multi-Target Detection and Tracking.

In modern radar detection systems, the particle filter technique has become one of the core algorithms for real-time target detection and tracking due to its good nonlinear and non-Gaussian system state estimation capability. However, when dealing with complex dynamic scenes, the traditional particle filter algorithm exposes obvious deficiencies. The main expression is that the sample degradation is serious, which leads to a decrease in estimation accuracy. In multi-target states, the algorithm is difficult to effectively distinguish and stably track each target, which increases the difficulty of state estimation. These problems limit the application potential of particle filter technology in multi-target complex environments, and there is an urgent need to develop a more advanced algorithmic framework to enhance its robustness and accuracy in complex scenes. Therefore, this paper proposes an improved particle filter algorithm for multi-target detection and tracking. Firstly, the particles are divided into tracking particles and searching particles. The tracking particles are used to maintain and update the trajectory information of the target, and the searching particles are used to identify and screen out multiple potential targets in the environment, to sufficiently improve the diversity of the particles. Secondly, the density-based spatial clustering of applications with noise is integrated into the resampling phase to improve the efficiency and accuracy of particle replication, so that the algorithm can effectively track multiple targets. Experimental result shows that the proposed algorithm can effectively improve the detection probability, and it has a lower root mean square error (RMSE) and a stronger adaptability to multi-target situation.

A Proportional–Integral Observer-Based Dynamic Event-Triggered Consensus Protocol for Nonlinear Positive Multi-Agent Systems

This paper investigates the state estimation and event-triggered control for positive nonlinear multi-agent systems. Firstly, a proportional–integral observer is established to estimate the states of the considered nonlinear positive multi-agent systems based on the matrix decomposition method. Then, a dynamic event-triggered mechanism is constructed, and a control protocol is proposed based on the proportional–integral observer and event-triggered mechanism. By combining linear programming with linear co-positive Lyapunov functions, the considered multi-agent systems are guaranteed to be positive and achieve consensus. Moreover, by introducing three new variables and a finite vector, the final convergence point can be changed based on the given vector. Finally, two illustrative examples demonstrate the validity of the proposed theoretical results.

A class of adaptive predefined‐time extended state observers for high‐order strict‐feedback systems

AbstractFast state estimation for nonlinear systems has been a key issue in control theory and the recently developed predefined‐time stability acts as an effective tool for the problem. However, the studies of predefined‐time state observer for nonlinear systems are rare. In this article, we consider the predefined‐time extended state observer (PTESO) design for a class of high‐order strict‐feedback systems subject to Hölder continuous nonlinearities and lumped disturbance. By developing an adaptive mechanism and using time‐varying functions, a class of adaptive PTESOs is designed to estimate the unavailable states and the lumped disturbance, in which the convergence time can be tightly and explicitly preset by only one parameter, irrelevant to the initial conditions. The adaptive mechanism is used to improve the transient performance under wide‐range lumped disturbance. Moreover, thanks to the design of the time‐varying gains, the PTESO could realize fast observation with trivial peaking observation errors. Finally, simulation results are provided to illustrate the effectiveness of the proposed observer.

Cluster-based Bayesian approach for noisy and sparse data: application to flow-state estimation

This study presents a cluster-based Bayesian methodology for state estimation under realistic conditions including noisy data from sparse sensors. The proposed approach is interpretable and, building upon previous work on transition networks, explicitly accounts for experimental noise within the data-driven framework by means of data clustering. Experimental measurements are exploited, beyond model training, to quantify the degree of uncertainty (noise) for each trained state. Such noise levels are eventually associated with probability distributions that, when combined with Bayes’ theorem, allow us to perform real-time state estimation. The proposed methodology is tested on two cases of challenging flows generated by an accelerating elliptical plate and also a delta wing experiencing gusts. Results specifically indicate that the proposed approach is robust against the number of clusters, enabling state estimation with a significant order reduction, notably decreasing the computational cost while preserving estimation accuracy. Based on the present findings, the proposed data-driven approach can be employed for realistic state estimation in nonlinear systems where noise, sensor sparsity and nonlinearities represent a challenging scenario.

Online state and unknown inputs estimation for nonlinear systems with particle filter based recursive expectation‐maximization algorithm

AbstractThe article presents an innovative approach to simultaneously estimate states and unknown inputs (UIs) in nonlinear systems using a particle filter (PF) based recursive expectation‐maximization (EM) algorithm. This method is distinct from traditional iterative EM algorithms. During the E‐step, it calculates the Q‐function recursively within the maximum likelihood framework, while the PF estimates the system states. The M‐step involves local maximization of the recursive Q‐function to online estimate the UIs. The effectiveness of the PF‐based recursive EM algorithm is demonstrated with a numerical example, and comparisons with the augmented state PF are made to highlight its advantages. Finally, the proposed algorithm is implemented in a real application for the estimation of the continuous fermentation process.

Sampling free iterative PCE filter for state and parameter estimation of nonlinear dynamical systems

We present a novel filter for state and parameter estimation in non-linear dynamical systems, based on a generalised Kalman filter formulation. To achieve a sampling-free implementation, polynomial chaos expansion (PCE) and a Galerkin projection method are utilized for the propagation of uncertainties through the system dynamics. The non-linear dynamics of the system are then linearised by a sequence of Gauss-Newton iterations in combination with linear Kalman updates. Additionally, we introduce a new square root implementation of the PCE-based filter. The proposed filter is evaluated on the Lorenz-63 and Lorenz-84 models for the task of simultaneous state and parameter estimation and is compared with two related approaches. Finally, the computational complexity of our square-root implementation is compared against two existing square root approaches.

Simultaneous robust model predictive control and state estimation for nonlinear systems with state‐ and input‐dependent uncertainties

AbstractThe convergence and stability of uncertain nonlinear systems is a challenging problem in the nonlinear control area. Besides, in many practical cases, all states are not measurable and are affected by measurement noise. Based on this motivation, the first objective of this paper is to design a novel output feedback robust model predictive control approach for nonlinear systems with state‐ and input‐dependent uncertainties and measurement noise. This approach combines state estimation and robust model predictive control (MPC) into one min–max optimization and by solving the optimization, these two tasks are performed simultaneously. The studied nonlinear system comprises a linear part, a nonlinear part, and a function that denotes the state‐ and input‐dependent uncertainties. Therefore, the other objective is to reduce the computational complexity; thus, the system's nonlinear term and the aforementioned uncertainties are converted into additional disturbances. Subsequently, the optimization problem becomes a quadratic form, which leads to global convergence with the appropriate selection of objective function weights. Besides, this paper explores the convergence of the closed‐loop system states and the sufficient synthesis conditions to guarantee input‐to‐state stability. The implementation on a numerical example and a CSTR process demonstrate the applicability and reliability of the proposed approach.

Reducing the wrapping effect of set computation via Delaunay triangulation for guaranteed state estimation of nonlinear discrete-time systems

Set computation methods have been widely used to compute reachable sets, design invariant sets and estimate system state for dynamic systems. The wrapping effect of such set computation methods plays an essential role in the accuracy of their solutions. This paper studies the wrapping effect of existing interval, zonotopic and polytopic set computation methods and proposes novel approaches to reduce the wrapping effect for these set computation methods based on the task of computing the dynamic evolution of a nonlinear uncertain discrete-time system with a set as the initial state. The proposed novel approaches include the partition of a polytopic set via Delaunay triangulation and also the representation of a polytopic set by the union of small zonotopes for the following set propagation. The proposed novel approaches with the reduced wrapping effect has been further applied to state estimation of a nonlinear uncertain discrete-time system with improved accuracy. Similar to bisection for interval and zonotopic sets, Delaunay triangulation has been introduced as a set partition tool for polytopic sets, which has opened new research directions in terms of novel set partition, set representation and set propagation for reducing the wrapping effect of set computation.

Continuous–discrete derivative-free extended Kalman filter based on Euler–Maruyama and Itô–Taylor discretizations: Conventional and square-root implementations

In this paper, we continue to study the derivative-free extended Kalman filtering (DF-EKF) framework for state estimation of continuous–discrete nonlinear stochastic systems. Having considered the Euler–Maruyama and Itô–Taylor discretization schemes for solving stochastic differential equations, we derive the related filters’ moment equations based on the derivative-free EKF principal. In contrast to the recently derived MATLAB-based continuous–discrete DF-EKF techniques, the novel DF-EKF methods preserve an information about the underlying stochastic process and provide the estimation procedure for a fixed number of iterates at the propagation steps. Additionally, the DF-EKF approach is particularly effective for working with stochastic systems with highly nonlinear and/or nondifferentiable drift and observation functions, but the price to be paid is its degraded numerical stability (to roundoff) compared to the standard EKF framework. To eliminate the mentioned pitfall of the derivative-free EKF methodology, we develop the conventional algorithms together with their stable square-root implementation methods. In contrast to the published DF-EKF results, the new square-root techniques are derived within both the Cholesky and singular value decompositions. A performance of the novel filters is demonstrated on a number of numerical tests including well- and ill-conditioned scenarios.

In-context learning of state estimators

State estimation has a pivotal role in several applications, including but not limited to advanced control design. Especially when dealing with nonlinear systems state estimation is a nontrivial task, often entailing approximations and challenging fine-tuning phases. In this work, we propose to overcome these challenges by formulating an in-context state-estimation problem, enabling us to learn a state estimator for a class of (nonlinear) systems abstracting from particular instances of the state seen during training. To this end, we extend an in-context learning framework recently proposed for system identification, showing via a benchmark numerical example that this approach allows us to (i) use training data directly for the design of the state estimator, (ii) not requiring extensive fine-tuning procedures, while (iii) achieving superior performance compared to state-of-the-art benchmarks.

Set-valued state estimation of nonlinear discrete-time systems and its application to attack detection

Set-valued state estimation of nonlinear discrete-time systems and its application to attack detection

STATE ESTIMATION FOR A CLASS OF FRACTIONAL-ORDER UNCERTAIN NONLINEAR SYSTEMS

The robust state estimation problem for a class of fractional-order uncertain non- linear systems is investigated in this paper. The class of fractional-order uncertain nonlinear systems is more general than the existing one in the literature. For the first time, a method based on a new fractional-order state observer is proposed to give robust state estimation of the fractional-order uncertain nonlinear systems. A new condition for the existence of the fractional-order observer in terms of an optimization problem is proposed. The effectiveness of the proposed method is demonstrated through two examples.

On the state estimation for nonlinear continuous-time fuzzy systems

On the state estimation for nonlinear continuous-time fuzzy systems

Adaptive Set-Membership State Estimation for Nonlinear Systems Under Bit Rate Allocation Mechanism: A Neural-Network-Based Approach.

In this article, the adaptive neural-network-based (NN-based) set-membership state estimation problem is studied for a class of nonlinear systems subject to bit rate constraints and unknown-but-bounded noises. The measurement output signals are transmitted from sensors to a remote estimator via a bit rate constrained communication channel. To relieve the communication burden and ameliorate the state estimation accuracy, a bit rate allocation mechanism is put forward for the sensor nodes by solving a constrained optimization problem. Subsequently, through the NN learning method, an NN-based set-membership estimator is designed to determine an ellipsoidal set that contains the system state, where the proposed estimator relies upon a prediction-correction structure. With the help of the mathematical induction technique and the set theory, sufficient conditions are obtained to ensure the existence of both the adaptive tuning parameters and the set-membership estimators, and then, the corresponding parameters and estimator gains are calculated by solving a set of optimization problems. In addition, the monotonicity of the upper bound on the squared estimation error with respect to the bit rate and the convergence of the NN weight are analyzed, respectively. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed state estimation algorithm.

Nonlinear event-based state estimation using particle filter under packet loss

In this research paper, we investigate the problem of remote state estimation for nonlinear discrete systems. Specifically, we focus on scenarios where event-triggered sensor schedules are utilized and where packet drops occur between the sensor and the estimator. In the sensor scheduler, the SOD mechanism is proposed to decrease the amount of data transmitted from the sensor to a remote estimator and the phenomena of packet drops modeled with random variables obeying the Bernoulli distribution. As a consequence of packet drops, the assumption of Gaussianity no longer holds at the estimator side. By fully considering the non-linearity and non-Gaussianity of the dynamic system, this paper develops an event-trigger particle filter algorithm to relieve the communication burden and achieve an appropriate estimation accuracy. First, we derive an explicit expression for the likelihood function when an event trigger occurs and the possible occurrence of packet dropout is taken into consideration. Then, using a special form of sequential Monte–Carlo algorithm, the posterior distribution is approximated and the corresponding minimum mean-squared error is derived. By contrasting the error covariance matrix with the posterior Cramér–Rao lower bound, the estimator’s performance is assessed. An illustrative numerical example shows the effectiveness of the proposed design.

Event-triggered state and fault simultaneous estimation for nonlinear systems with time delays

This paper addresses the problem of event-triggered robust state and fault simultaneous estimation for nonlinear time-delay systems subject to actuator and sensor unknown disturbances. Based on a fault decomposition technique and some basic mathematical transformations, we obtain an augmented system where the state vector consists of the variable of the original system and the fault. Then a novel event-triggered state observer for the augmented system is proposed to robustly estimate the variable of the original system and the fault. We next established a sufficient condition for the existence of such an observer. We translated it into a linear matrix inequality (LMI), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, an illustrative example is applied to test the proposed method.

Enhanced square root CKF with mixture correntropy loss for robust state of charge estimation of lithium-ion battery

The measurement data of lithium-ion battery collected in complex operating conditions may be contaminated by non-Gaussian noises (or outliers), a novel robust state of charge (SOC) estimation approach that enhances the robustness of square-root cubature Kalman filter (SRCKF) by incorporating a mixture correntropy loss (MCL) is proposed to overcome the issue of non-Gaussian measurement noise interference. Although the SRCKF can perform non-destructive state estimation for nonlinear system, it is sensitive to the non-Gaussian noises (or outliers) due to the use of mean square error (MSE) loss. To overcome this limitation, the MCL is used as a cost to replace the MSE in CKF framework, which is constructed by mixture of two Gaussian kernel functions with different kernel widths and has outstanding robustness. Moreover, we establish an effective nonlinear regression model that incorporates noise and state error information into the MCL function, and then a fixed-point iteration method is utilized to update the posterior state estimation. Additionally, to further suppress the influence of abnormal noise on the posterior state estimation, we introduce the exponential function of the innovation vector to adjust the measurement covariance matrix in real-time. Accordingly, an enhanced MCL-SRCKF is developed for SOC estimation considering the measurement noises with non-Gaussian distribution. Results from various simulation environments demonstrate that the proposed method achieves high estimation accuracy in different cases.

Joint state and fault estimation for nonlinear systems with missing measurements and random component faults under Round-Robin Protocol

This work studies the fault estimation problem for a class of nonlinear systems subjected to missing measurements and random component faults under the Round-Robin protocol. Considering that the communication bandwidth is not infinite in the actual projects, the Round-Robin protocol is used for data scheduling, in which sensor nodes cyclically transmit data to the controller/filter. Meanwhile, component faults are also considered which usually caused by actuator faults. It should be emphasized that the introduction of RR protocol will make the system output equation more complex, the MMs and component faults will generate more unknown parameters, which will bring new challenges during the design of the filter. In respect of the problems above, a recursive joint state and fault estimation (JSFE) algorithm is proposed to solve the difficulties caused by missing measurements, component faults, and nonlinearity. The performance of the designed JSFE filter is analyzed by using the boundedness theorem and the reasonable parameter condition is derived for this filter. Finally, an engineering example is given to verify the effectiveness and feasibility of the proposed joint state and fault estimation scheme. This study provides a new theoretical basis and reference for the JSFE of nonlinear systems with mixed faults under RR protocol.

Approximate current state observability of discrete-time nonlinear systems under cyber-attacks

Widespread use of the Internet and other means of communication has increased the risk of cyber-attacks that can affect the warranted operation of a system. To prevent damages from attacks, an assessment of its security plays an important role in providing fast and reliable solutions. This paper focuses on state estimation of nonlinear systems under attacks. We consider a plant represented by a discrete-time nonlinear system and an attacker modeled as a finite state machine. We propose a novel notion of observability, called approximate current state observability under attacks, which corresponds to the possibility of identifying the current state of the plant after a given transient despite the malicious action of an attacker that can replace the plant output symbols in the communication network infrastructure. To provide conditions for this property to hold, we resort to the use of formal methods and in particular, of symbolic models. Symbolic models provide an abstract description of purely continuous systems, where a symbolic state corresponds to an aggregate of continuous states in the original system. The approach we propose is particularly useful when dealing with cyber-security of continuous processes in that it offers a framework to deal with the heterogeneous models of the plant and the attacker. An academic example showing the applicability of the results presented is included.