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

Event-triggered adaptive fault estimation and fault-tolerant control for strict-feedback nonlinear systems with full state constraints

Event-triggered adaptive fault estimation and fault-tolerant control for strict-feedback nonlinear systems with full state constraints

Enhanced tracking control for n-DOF robotic manipulators: A fixed-time terminal sliding mode approach with time delay estimation

This work proposes a fixed-time terminal sliding mode control scheme with time delay estimation (FxTSM-TDE) for unknown nonlinear robotic systems under uncertainties and unknown bounded disturbances. The idea of the fixed-time terminal sliding mode control method (FxTSM) is thoroughly explained and analyzed. The FxTSM approach has been used to achieve nonsingular fixed-time control, non-chatter control inputs, and superior trajectory tracking performance. Then, the proposed approach for estimating the unknown robot dynamics utilizes the TDE approach. The Lyapunov analysis is used to establish the fixed-time stability of the system. The effectiveness of the suggested approach is evaluated, demonstrated, and contrasted with the existing control schemes by illustrating the results of the proposed method's enhanced performance in tracking accuracy, robustness, and convergence speed when implemented in robotic manipulator dynamics. The results indicate that the existing scheme has corresponding root mean square (RMS) error values of 0.0235 and 0.0283, while the proposed scheme has values of 0.0178 and 0.0188, respectively.

Distributed fault estimation of nonlinear dynamical systems over sensor networks: a non-fragile approach

Distributed fault estimation of nonlinear dynamical systems over sensor networks: a non-fragile approach

Integrated Fault-Tolerant Control Design With Sampled-Output Measurements for Interval Type-2 Takagi-Sugeno Fuzzy Systems.

This article is concerned with the integrated design of fault estimation (FE) and fault-tolerant control (FTC) for uncertain nonlinear systems suffering from actuator faults and external disturbance. The uncertain nonlinear systems are characterized as the interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy model, and IT2 membership functions are employed to effectively handle uncertainties. A fuzzy observer, utilizing only sampled-output measurements, is applied to simultaneously estimate actuator faults and system states. Based on the estimation, the fault-tolerant controller is designed to ensure the system stability under a predefined H∞ performance. The sampling behavior complicates the system dynamics and makes the integrated FTC design more challenging. To confront this issue, the discontinuous Lyapunov functional technique is exploited to enhance stability results by considering the sampling characteristic, upon which FE and FTC units are co-designed in the linear matrix inequality (LMI) framework. To further relax stability criteria, the analysis process incorporates the bound information of membership functions through the membership-function-dependent (MFD) method. Additionally, the relationship of mismatched premise variables resulting from the sampling scheme is also taken into account. Moreover, considering the imperfect premise matching (IPM) framework, the proposed fault-tolerant controller provides greater flexibility in selecting the shapes of membership functions and number of fuzzy rules that can vary from the counterpart of the fuzzy system. Finally, the efficacy of the proposed FTC technique is validated through a detailed numerical example.

Command filter–based fixed-time fault estimation and compensation control for nonlinear systems with prescribed performance

Command filter–based fixed-time fault estimation and compensation control for nonlinear systems with prescribed performance

H_∞ Estimation of Nonlinear Time-Varying Systems with Data Packet Dropouts

H_∞ Estimation of Nonlinear Time-Varying Systems with Data Packet Dropouts

Distributed Fault Estimation for Nonlinear Systems With Sensor Saturation and Deception Attacks Using Stochastic Communication Protocols

Distributed Fault Estimation for Nonlinear Systems With Sensor Saturation and Deception Attacks Using Stochastic Communication Protocols

Neural network-based adaptive fault-tolerant control for nonlinear systems with uncertainties

This paper proposes a novel fault-tolerant control (FTC) scheme for real-time uncertainty estimation in nonlinear systems. It addresses the challenges arising from nonlinear dynamics in system inputs, states, and outputs, along with measurement uncertainties, within an output feedback framework. Our approach leverages two key components: 1) A neural network NN descriptor-based observer: this novel observer concurrently estimates both system states and sensor uncertainties. It is particularly capable of handling unbounded sensor uncertainties in specific situations. It utilizes NNs as universal approximators to capture the system's complex nonlinearities. 2) A robust model reference tracking controller: this controller employs the estimated states from the NN descriptor-based observer to achieve the desired system performance despite the existence of uncertainties. It exhibits robustness, guaranteeing system stability and asymptotic state tracking to a given reference model. The efficacy of the proposed FTC scheme is validated through theoretical analysis and its application to two real-world case studies.

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.

An iterative interval estimation approach to nonlinear discrete-time systems

This paper is devoted to the iterative interval estimation for nonlinear discrete-time systems. To reconstruct the system state, a sequence of iterative observers is established based on the iterative disturbance estimation and measured output. By means of the Lipschitz condition and [Formula: see text] technique, sufficient conditions are built by the Lyapunov function method to make observation errors convergent. Resorting to the zonotope-based reachability analysis, the reachable set of nonlinear terms and observation errors are analyzed such that the state interval can be supplied. The presented approach is validated by a simulation comparison.

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.

Novel intelligent supervised neuro-structures for nonlinear financial crime differential systems

Artificial intelligence (AI)-based applications contribute to monitoring financial transactions and detect fraudulent activity in real-time by analyzing transaction patterns, consumer behavior, and other statistics, making them essential for quickly addressing potential threats in the fight against financial crime dynamics. Leveraging financial crime systems with intelligent supervised neuro-structures exploiting nonlinear autoregressive exogenous networks integrating damped least square (NARX-DLS) optimization methods to achieve an appropriate degree of accuracy and adaptability for the estimation of complex nonlinear financial crime differential systems (NFCDSs). The representative NFCDS for financial crime indicators is expressed as susceptible individuals, financial criminals, individuals under prosecution, imprisoned individuals, and honest individuals. The Adams numerical solver accomplishes the acquisition of synthetic data for the layer structure NARX-DLS algorithm execution to solve NFCDSs for various financial crime parameters, such as recruitment rate, influence rate, conversion rate to honest people, financial criminal prosecution rate per capita, discharge and acquittal rate from prosecutions, percentage of discharge rate from prosecution, transition rate to prison, and freedom rate. A sturdy overlap between the solutions of NARX-DLSs and the reference numerical results of NFCDSs implies that the error value is close to a desirable value of zero. The effectiveness of the NARX-DLSs is evidenced by including a variety of assessment metrics that carefully examine the model’s correctness and efficacy, including mean square error-based convergence arches, adaptive regulating parameters, error distribution, and input-error/cross-correlation analyses.

Torus-Event-Based Fault Estimation for Stochastic Nonlinear Systems with Randomly Occurring Saturation and Missing Measurements

Torus-Event-Based Fault Estimation for Stochastic Nonlinear Systems with Randomly Occurring Saturation and Missing Measurements

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.

Parameter estimation for fractional-order nonlinear systems based on improved sparrow search algorithm

Parameter estimation is important in the study of control and synchronization of fractional-order nonlinear systems (FONSs). This paper proposes an improved Sparrow Search Algorithm (ISSA) for the parameter estimation problem of FONSs. The algorithm improves the population initialization, position update method of discoverers and warning sparrows based on Sparrow Search Algorithm (SSA), and the parameter estimation simulation experiment for fractional-order financial nonlinear system and fractional-order L nonlinear system is conducted to demonstrate this method. The experimental results show that the proposed ISSA is superior to the SSA, Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA) and Harris Hawks Optimization (HHO) in terms of parameter optimization accuracy and convergence speed, which validates the advantages of the ISSA.

An improved Cauchy robust correction-sage Husa extended Kalman filtering algorithm for high-precision SOC estimation of Lithium-ion batteries in new energy vehicles

The accurate estimation of battery State of Charge (SOC) is a key technology in the research of electric vehicle battery management systems. In order to solve the problem of inaccurate noise estimation in nonlinear systems, an improved Cauchy robust correction-Sage Husa extended Kalman filtering (CRC-SHEKF) algorithm is proposed for high-precision SOC estimation of lithium-ion batteries in new energy vehicles. Considering the polarization effect of the battery, the FFRLS algorithm is used for online parameter identification of the Dual Polarization model. Using robust data correction methods, the Cauchy robust function is simplified for real-time correction of the covariance matrix Q of system state noise and the covariance matrix R of the observed noise in the filtering process and combined with SHEKF for SOC estimation. The experimental results show that under different temperature conditions and complex working conditions, the proposed CRC-SHEKF algorithm has the minimum mean absolute error (MAE), root mean square error (RMSE), and maximum error (MAX). Under the condition of the Beijing bus dynamic stress test (BBDST) at 15 °C, the MAE, RMSE, and MAX of the CRC-SHEKF algorithm are 0.392 %, 0.716 %, and 0.945 %, with the computing time of only 4.839 s. The algorithm proposed in this article has high accuracy and robustness, and has practical application value, providing a reference for the application of lithium battery condition monitoring.