Estimation Of Nonlinear Systems Research Articles

Multi-layer CNN-LSTM network with self-attention mechanism for robust estimation of nonlinear uncertain systems.

With the help of robot technology, intelligent rehabilitation of patients with lower limb motor dysfunction caused by stroke can be realized. A key factor constraining the clinical application of rehabilitation robots is how to realize pattern recognition of human movement intentions by using the surface electromyography (sEMG) sensors to ensure unhindered human-robot interaction. A multilayer CNN-LSTM prediction network incorporating the self-attention mechanism (SAM) is proposed, in this paper, which can extract and learn the periodic and trend characteristics of the sEMG signals, and realize the accurate autoregressive prediction of the human motion information. Firstly, the multilayer CNN-LSTM network utilizes the CNN layer for initial feature extraction of data, and the LSTM network is used to improve the enhancement of the historical time-series features. Then, the SAM is used to improve the global feature extraction performance and parallel computation speed of the network. In comparison with existing test is carried out using actual data from five healthy subjects as well as a clinical hemiplegic patient to verify the superiority and practicality of the proposed algorithm. The results show that most of the model's prediction R > 0.9 for different motion states of healthy subjects; in the experiments oriented to the motion characteristics of patient subjects, the angle prediction results of R > 0.99 for the untrained data on the affected side, which proves that our proposed model also has a better effect on the angle prediction of the affected side. The main contribution of this paper is to realize continuous motion estimation of ankle joint for healthy and hemiplegic individuals under non-ideal conditions (weak sEMG signals, muscle fatigue, high muscle tension, etc.), which improves the pattern recognition accuracy and robustness of the sEMG sensor-based system.

Zonotopic interval estimation for nonlinear systems with event-triggered protocols

This paper investigates the zonotope-based interval estimation problem for event-triggered nonlinear systems with incrementally quadratic constraint and unknown-but-bounded uncertainties from process disturbance and measurement noise. Considering the restricted communication bandwidth, an event-triggered communication protocol is deployed in the sensor-to-observer channel, based on which an event-triggered observer is constructed for nonlinear systems having incremental quadratic constraints. A co-design method of nonlinear observer and event-triggered protocol is obtained to ensure the stability and ℓ∞ index of the estimation error dynamic. Based on the designed event-triggered observer, a zonotope-based interval estimation algorithm is designed for the purpose of giving the intervals enclosing admissible values of system state. The mean value extension coalesce into natural interval extension is utilized to deal with the nonlinear transformation of system, and the enclosing zonotope of ellipsoid is introduced to tackle the extra uncertainties induced by event-triggered protocol. Lastly, the results of a simulation on a hyper-chaotic Chen system are provided to confirm the validity of the presented methodology.

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.

Fault estimation for a class of nonlinear systems using the improved intermediate estimator

AbstractThis paper focused on fault estimation in Lipschitz nonlinear systems by providing an improved intermediate estimator (IIE). The core feature of an intermediate estimator is to simultaneously estimate the fault and states of the system without considering the matching condition. Since fault estimation is the first step of the process to compensate for its effect, the system performance can be further improved by making more accurate fault estimation. The structure of the nominal intermediate estimator (NIE) was modified by being inspired by the proportional‐integral (PI) controller to improve the performance characteristics of the estimator, such as convergence rate, overshoot, and steady‐state error. The estimation equation was assumed as such in the proposed estimator structure that the estimated fault would have a PI structure of the output estimation error. This has increased the number of design parameters, improving the estimator performance in transient and steady‐state. The NIE can be indeed known as a particular case of the IIE since the proposed estimator benefits from all the advantages of an NIE while improving the estimation performance. The states of the error system were proven to be uniformly ultimately bounded according to Lyapunov stability theory and using the LMI method, as well as the appropriate selection of parameters. The analysis of the theory, simulation, and comparing the results of the proposed method with the NIE method reveal the capabilities and advantages of the proposed method.

A posteriori error estimation for model order reduction of parametric systems

AbstractThis survey discusses a posteriori error estimation for model order reduction of parametric systems, including linear and nonlinear, time-dependent and steady systems. We focus on introducing the error estimators we have proposed in the past few years and comparing them with the most related error estimators from the literature. For a clearer comparison, we have translated some existing error bounds proposed in function spaces into the vector space $${\mathbb {C}}^n$$ C n and provide the corresponding proofs in $$\mathbb C^n$$ C n . Some new insights into our proposed error estimators are explored. Moreover, we review our newly proposed error estimator for nonlinear time-evolution systems, which is applicable to reduced-order models solved by arbitrary time-integration solvers. Our recent work on multi-fidelity error estimation is also briefly discussed. Finally, we derive a new inf-sup-constant-free output error estimator for nonlinear time-evolution systems. Numerical results for three examples show the robustness of the new error estimator.

An estimation method for sensor faults based on observer in interconnected systems.

In this research, a class of nonlinear interconnected systems with sensor faults were investigated and an estimation method was proposed for system sensor faults based on the theory of system state reconstruction. Considering sensor fault vectors in nonlinear interconnected systems, this method constructed a generalized nonlinear interconnected system, whose state was designed by augmenting the original system state and fault vectors, which provides a foundation for fault estimation of nonlinear interconnected systems. An augmented observer was developed by equivalent transformation of generalized interconnected system, so as to realize robust estimations of sensor faults in interconnected systems. This estimation method took into account the effect of external disturbance of the system on fault estimation and estimated the convergence speed of error system; the developed method also considered the convenience of solving the gain matrix of the augmented observer, which was beneficial to the realization of sensor fault estimation in interconnected system. The sensor estimation method proposed in the paper has the advantages of robustness in fault estimation,rapidity in error convergence, and convenience in solving the gain matrix. Finally, the state and sensor fault estimation errors of two interconnected systems can both approach 0 within 10 seconds, thus achieving the purpose of fault estimation. Two simulation experiments verified the effectiveness of the proposed fault estimation method and provided a reference for the fault estimation method of nonlinear interconnected systems with disturbance.

Fault estimation for nonlinear uncertain systems utilizing neural network-based robust iterative learning scheme

Fault estimation for nonlinear uncertain systems utilizing neural network-based robust iterative learning scheme

Estimation of wiener nonlinear systems with measurement noises utilizing correlation analysis and Kalman filter

AbstractThis paper is concerned with parameter estimation of Wiener systems with measurement noises employing correlation analysis method and adaptive Kalman filter. The presented Wiener system consists of two series blocks, that is, a dynamic block represented by auto‐regressive moving average (ARMA) model, and static nonlinear block established by neural fuzzy model. Aim at estimating separately the two blocks, the separable signals are introduced. First, applying the separable signals to decouple the identification of linear dynamic block from that of static nonlinear block, then ARMA model parameters are estimated employing correlation function‐based least squares principle. Moreover, aiming at handle with error caused by colored measurement noise, adaptive Kalman filter technique and cluster method are introduced to estimate parameter of the nonlinear block and noises model, enhancing parameter estimation precision. The accuracy and applicability of estimated scheme presented are verified through numerical simulation and nonlinear process, the results demonstrate that it is feasible for estimating the Wiener systems in the presence of colored measurement noises.

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.

Parameter estimation of multivariable Wiener nonlinear systems by the improved particle swarm optimization and coupling identification

This paper investigates the parameter estimation of multivariable Wiener nonlinear systems. To solve the inconsistency problem of the parameter vector and the parameter matrix, the coupling identification concept is applied. Combined with particle swarm optimization (PSO) and an auxiliary model, the partially coupled improved particle swarm optimization (PC-IPSO) method is proposed. In this algorithm, the adaptive feedback inertia weight is improved to accelerate the convergence speed, and the retirement update mechanism is introduced to improve the optimization ability of the basic PSO algorithm. To verify the performance of PC-IPSO, we also derive a multivariable improved PSO (M-IPSO) method for comparison. The computational complexity analysis shows that the PC-IPSO algorithm requires less computational resources than the M-IPSO algorithm. Then, the convergence of the improved PSO method is analyzed. The simulation results indicate that the PC-IPSO method has a faster convergence speed and higher identification accuracy than the M-IPSO and several existing state-of-the-art methods for multivariable Wiener system identification.

Event-Triggered State Filter Estimation for Nonlinear Systems with Packet Dropout and Correlated Noise

This paper begins by exploring the challenge of event-triggered state estimations in nonlinear systems, grappling with packet dropout and correlated noise. A communication mechanism is introduced that determines whether to transmit measurement values based on whether event-triggered conditions are violated, thereby minimizing redundant communication data. In designing the filter, noise decorrelation is initially conducted, followed by the integration of the event-triggered mechanism and the unreliable network transmission system for state estimator development. Subsequently, by combining the three-degree spherical–radial cubature rule, the numerical implementation steps of the proposed state estimation framework are outlined. The performance estimation analysis highlights that by adjusting the event-triggered threshold appropriately, the estimation performance and transmission rate can be effectively balanced. It is established that when there is a lower bound on the packet dropout rate, the covariance matrix of the state estimation error remains bounded, and the stochastic stability of the state estimation error is also confirmed. Ultimately, the algorithm and conclusions that are proposed in this paper are validated through a simulation example of a target tracking system.

Fault estimation for nonlinear uncertain time‐delay systems based on unknown input observer

AbstractIn this paper, a novel nonlinear unknown input observer is proposed in order to fault estimation for nonlinear uncertain systems with time delays. By the estimation of the faults, the features are detected such as shape, size occurrence time etc. The time delay is considered a constant and known parameter in the states. The disturbances are investigated in the states and outputs and also, and sensor and actuator faults are considered. The stability of the closed‐loop system is guaranteed by Lyapunov–Krasovskii theory and some feasible Linear matrix inequalities (LMI). The proposed method is simulated on a continuous‐stirred tank reactor (CSTR) with uncertainties and time delay. Simulation results show the appropriate efficiency of the proposed method.

Zonotopic non-fragile set-membership fusion estimation for nonlinear systems under sensor resolution effects: Boundedness and monotonicity

In this paper, the zonotopic non-fragile set-membership fusion estimation problem is investigated for multi-sensor nonlinear systems under sensor resolution effects. The sensor resolutions, which characterize the smallest change of signals that can be detected by sensors, are considered to reflect the engineering practice. A sequential fusion estimator, which takes the possible estimator gain variations (PEGVs) into account, is constructed to estimate the system state. Based on the mean value theorem and the first-order Taylor expansion, a novel method is first proposed to derive a zonotope containing the one-step prediction error, and such a method is proven to be beneficial in improving the prediction accuracy. Then, a PEGV-dependent zonotope is derived to enclose the estimation error after each measurement update, and the estimator parameter is designed to minimize a certain upper bound of the F-radius of the derived zonotope. Subsequently, in order to acquire bounds of the system states, a PEGV-independent zonotope is obtained at each time instant to enclose the estimation error after the measurement update. Moreover, the monotonicity of the F-radius of the PEGV-independent zonotope is analyzed with regard to, respectively, the corresponding sensor resolution and the PEGV. Finally, two numerical examples are provided to show the effectiveness of the proposed fusion estimation method.

An efficient method for generalised Wiener series estimation of nonlinear systems using Gaussian processes

System identification of dynamical systems aims to predict the output of a system for a given input by inferring model details from data. This is particularly challenging for nonlinear vibrating systems with long memory, which often have complex dynamics for which the physics is not fully understood. However, in many engineering applications, it is important to capture as much of the nonlinearity in the response as possible. The Wiener series is a classical data-driven technique that decomposes the system response into a set of orthogonal functionals of increasing order. Unlike standard black-box algorithms, such as neural networks, the series is highly interpretable and can offer insight into the nonlinearities present. However, current methods require vast quantities of data to calculate higher order terms in the Wiener series. In this paper, a novel generalised formulation of the Wiener series is developed by framing the series explicitly as a QR decomposition. Then by placing a Gaussian process prior over the kernels, their inherent structure is exploited to significantly reduce the quantity of data required for inference. Initial investigations were carried out using two systems: first pre-defined kernels and second an idealised nonlinear oscillatory system with unknown kernels. It is demonstrated that the Gaussian Process Generalised Wiener Series (GPGWS) enables the calculation of up to and including the third order kernel for systems with long memory and improves the robustness to noise.

Model-free scheme using time delay estimation with fixed-time FSMC for the nonlinear robot dynamics

<abstract><p>This paper presents a scheme of time-delay estimation (TDE) for unknown nonlinear robotic systems with uncertainty and external disturbances that utilizes fractional-order fixed-time sliding mode control (TDEFxFSMC). First, a detailed explanation and design concept of fractional-order fixed-time sliding mode control (FxFSMC) are provided. High performance tracking positions, non-chatter control inputs, and nonsingular fixed-time control are all realized with the FxSMC method. The proposed approach performs better and obtains superior performance when FxSMC is paired with fractional-order control. Furthermore, a TDE scheme is included in the suggested strategy to estimate the unknown nonlinear dynamics. Afterward, the suggested system's capacity to reach stability in fixed time is determined by using Lyapunov analyses. By showing the outcomes of the proposed technique applied to nonlinear robot dynamics, the efficacy of the recommended method is assessed, illustrated, and compared with the existing control scheme.</p></abstract>

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

Stabilization and decay rate estimation of nonlinear flexible marine riser system with the rotational inertia under nonlinear boundary controls

Stabilization and decay rate estimation of nonlinear flexible marine riser system with the rotational inertia under nonlinear boundary controls

Machine learning-based fault estimation of nonlinear descriptor systems

Machine learning-based fault estimation of nonlinear descriptor systems

Efficient delay and parameter estimation for nonlinear systems based on lifted IRK integrators with inexact Jacobians

Efficient delay and parameter estimation for nonlinear systems based on lifted IRK integrators with inexact Jacobians

基于滤波和递推的Hammerstein非线性系统估计与控制

基于滤波和递推的Hammerstein非线性系统估计与控制