Parametric estimation of interconnected nonlinear systems described by input-output mathematical models

In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems,which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.     

Noise covariance identification for time-varying and nonlinear systems

Kalman-based state estimators assume a priori knowledge of the covariance matrices of the process and observation noise. However, in most practical situations, noise statistics and initial conditions are often unknown and need to be estimated from measurement data. This paper presents an auto-covariance least-squares-based algorithm for noise and initial state error covariance estimation of large-scale linear time-varying (LTV) and nonlinear systems. Compared to existing auto-covariance least-squares based-algorithms, our method does not involve any approximations for LTV systems, has fewer parameters to determine and is more memory/computationally efficient for large-scale systems. For nonlinear systems, our algorithm uses full information estimation/moving horizon estimation instead of the extended Kalman filter, so that the stability and accuracy of noise covariance estimation for nonlinear systems can be guaranteed or improved, respectively.     

Adaptive estimation of discrete-time systems with nonlinear parameterization

This paper concerns adaptive estimation of dynamic systems which are nonlinearly parameterized. A majority of adaptive algorithms employ a gradient approach to determine the direction of adjustment, which ensures stable estimation when parameters occur linearly. These algorithms, however, do not suffice for estimation in systems with nonlinear parameterization. We introduce in this paper a new algorithm for such systems and show that it leads to globally stable estimation by employing a different regression vector and selecting a suitable step size. Both concave/convex parameterizations as well as general nonlinear parameterizations are considered. Stable estimation in the presence of both nonlinear parameters and linear parameters which may appear multiplicatively is established. For the case of concave/convex parameterizations, parameter convergence is shown to result under certain conditions of persistent excitation.     

Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory

This paper combines polynomial chaos theory with maximum likelihood estimation for a novel approach to recursive parameter estimation in state-space systems. A simulation study compares the proposed approach with the extended Kalman filter to estimate the value of an unknown damping coefficient of a nonlinear Van der Pol oscillator. The results of the simulation study suggest that the proposed polynomial chaos estimator gives comparable results to the filtering method but may be less sensitive to user-defined tuning parameters. Because this recursive estimator is applicable to linear and nonlinear dynamic systems, the authors portend that this novel formulation will be useful for a broad range of estimation problems.     

Adaptive nonlinear observer for state and unknown parameter estimation in noisy systems

This paper proposes a novel adaptive observer for Lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise. The observer is based on an H_∞ observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters. The paper presents necessary and sufficient conditions for the existence of the observer, and the equations for determining observer gains are formulated as linear matrix inequalities (LMIs) that can be solved offline using commercially available LMI solvers. The observer design has also been extended to the case of time-varying unknown parameters. The use of the observer is demonstrated through illustrative examples and the performance is compared with extended Kalman filtering. Compared to previous results on nonlinear observers, the proposed observer is more computationally efficient, and guarantees state and parameter estimation for two very broad classes of nonlinear systems (Lipschitz and dissipative nonlinear systems) in the presence of input disturbances and sensor noise. In addition, the proposed observer does not require online computation of the observer gain.     

基于改进的布谷鸟搜索算法对分数阶生物系统的参数估计

近年来,非线性分数阶系统的参数估计问题已经在许多科学和工程领域特别是计算生物学中,引起了广泛的兴趣.本文针对分数阶生物系统的参数估计问题,将系统参数和分数阶导数同时作为独立的未知参数来进行估计,并提出了一种改进的布谷鸟搜索(improved cuckoo search, ICS)算法来求解该问题.在ICS算法中,通过引入一个自适应参数控制机制,同时结合反向学习方法,从而达到提高算法收敛速度和估计值精度的目的.最后,以三种经典的分数阶生物动力系统模型为例进行了数值仿真,其中还考虑了有测量误差和噪声数据的情形.仿真结果表明ICS算法具有良好的适应性、较高的收敛可靠性及精度,为求解非线性分数阶系统参数估计问题提供了一种有效工具.     

Fuzzy system as parameter estimator of nonlinear dynamic functions

In this paper we use adaptive fuzzy systems as intelligent identification systems for nonlinear time-varying plants. A new technique to design the fuzzy system that relies on the minimization of a loss function is presented. The design technique uses the centers of the fuzzy sets (labels) at the antecedent part of the rule base as the estimated parameters. This parametrization has the Linear In The Parameters (LITPs) characteristic that allows standard parameter estimation technique to be used to estimate the parameters of the fuzzy system. The combination of the fuzzy system and the estimation method then performs as a nonlinear estimator. If several fuzzy sets are defined for the input variables at the antecedent part, the fuzzy system ("fuzzy estimator") then behaves as a collection of nonlinear estimators where different rules' regions have different parameters. The proposed scheme is potentially capable of estimating the parameters of highly nonlinear plants. Simulation examples, which use plants with highly nonlinear gain, show the power of the proposed estimation scheme in comparison to estimation using the linear model.     

Magnetic sensor-based simultaneous state and parameter estimation using a nonlinear observer

This paper presents an observer design technique for a newly developed non-intrusive position estimation system based on magnetic sensors. Typically, the magnetic field of an object as a function of position needs to be represented by a highly nonlinear measurement equation. Previous results on observer design for nonlinear systems have mostly assumed that the measurement equation is linear, even if the process dynamics are nonlinear. Hence, a new nonlinear observer design method for a Wiener system composed of a linear process model together with a nonlinear measurement equation is developed in this paper. First, the design of a two degree-of-freedom nonlinear observer is proposed that relies on a Lure system representation of the observer error dynamics. To improve the performance in the presence of parametric uncertainty in the measurement model, the nonlinear observer is augmented to estimate both the state and unknown parameters simultaneously. A rigorous nonlinear observability analysis is also presented to show that a dual sensor configuration is a sufficient and necessary condition for simultaneous state and parameter estimation. Finally, the developed observer design technique is applied to non-intrusive position estimation of the piston inside a pneumatic cylinder. Experimental results show that both position and unknown parameters can be reliably estimated in this application.     

&thetas;-adaptive neural networks: a new approach to parameterestimation

A novel use of neural networks for parameter estimation in nonlinear systems is proposed. The approximating ability of the neural network is used to identify the relation between system variables and parameters of a dynamic system. Two different algorithms, a block estimation method and a recursive estimation method, are proposed. The block estimation method consists of the training of a neural network to approximate the mapping between the system response and the system parameters which in turn is used to identify the parameters of the nonlinear system. In the second method, the neural network is used to determine a recursive algorithm to update the parameter estimate. Both methods are useful for parameter estimation in systems where either the structure of the nonlinearities present are unknown or when the parameters occur nonlinearly. Analytical conditions under which successful estimation can be carried but and several illustrative examples verifying the behavior of the algorithms through simulations are presented.     

Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems

This paper is concerned with an adaptive state estimation problem for a class of nonlinear stochastic systems with unknown constant parameters. These nonlinear systems have a linear-in-parameter structure, and the nonlinearity is assumed to be bounded in a Lipschitz-like manner. Using stochastic counterparts of Lyapunov stability theory, we present adaptive state and parameter estimators with ultimately exponentially bounded estimator errors in the sense of mean square for both continuous-time and discrete-time nonlinear stochastic systems. Sufficient conditions are given in terms of the solvability of LMIs. Moreover, we also introduce a suboptimal design approach to optimizing the upper bound of the mean-square error of parameter estimation. This suboptimal design procedure is also realized by LMI computations. By a martingale method, we also show that the related Lyapunov function has a non-negative Lyapunov exponent.     

Joint state and parameter robust estimation of stochastic nonlinear systems

Successful implementation of many control strategies is mainly based on accurate knowledge of the system and its parameters. Besides the stochastic nature of the systems, nonlinearity is one more feature that may be found in almost all physical systems. The application of extended Kalman filter for the joint state and parameter estimation of stochastic nonlinear systems is well known and widely spread. It is a known fact that in measurements, there are inconsistent observations with the largest part of population of observations (outliers). The presence of outliers can significantly reduce the efficiency of linear estimation algorithms derived on the assumptions that observations have Gaussian distributions. Hence, synthesis of robust algorithms is very important. Because of increased practical value in robust filtering as well as the rate of convergence, the modified extended Masreliez–Martin filter presents the natural frame for realization of the joint state and parameter estimator of nonlinear stochastic systems. The strong consistency is proved using the methodology of an associated ODE system. The behaviour of the new approach to joint estimation of states and unknown parameters of nonlinear systems in the case when measurements have non‐Gaussian distributions is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

A systematic approach to adaptive observer synthesis for nonlinearsystems

Geometric techniques of controller design for nonlinear systems have enjoyed great success. A serious shortcoming, however, has been the need for access to full-state feedback. This paper addresses the issue of state estimation from limited sensor measurements in the presence of parameter uncertainty. An adaptive nonlinear observer is suggested for Lipschitz nonlinear systems, and the stability of this observer is shown to be related to finding solutions to a quadratic inequality involving two variables. A coordinate transformation is used to reformulate this inequality as a linear matrix inequality. A systematic algorithm is presented, which checks for feasibility of a solution to the quadratic inequality and yields an observer whenever the solution is feasible. The state estimation errors then are guaranteed to converge to zero asymptotically. The convergence of the parameters, however, is determined by a persistence-of-excitation-type constraint     

基于粒子群优化算法的非线性系统模型参数估计

非线性模型的参数估计是较为困难的寻优问题,经典方法常会陷入局部极值。由于粒子群算法是一种有效的解决优化问题的群集智能算法,它的突出特点是操作简便、容易实现且全局搜索功能较强,故将粒子群优化算法用于非线性系统模型参数估计,并通过对3种典型的非线性模型的参数估计进行了验证。实验结果表明：粒子群优化算法参数估计精度高,是一种有效的参数估计方法。     

A prediction-error-method for recursive identification of nonlinear systems

Nonlinear systems can be identified with nonlinear filters by combined estimation of parameters and state. Often these methods are very complex or have convergence problems, as for example the Extended Kalman Filter. In this paper a new algorithm for recursive nonlinear system identification is presented. Convergence problems are eliminated by an improved calculation of the gradient as the total derivative of the prediction error. By separately estimating parameters and states, computation time is reduced. The efficacy of the new identification algorithm is illustrated by studying its performance in a gravimetric filling system.     

非线性系统参数估计的一类有效搜索策略

结合模拟退火的随机概率突跳性搜索和单纯形法的凸多面体几何搜索,提出了非线性 系统参数估计的一类有效搜索策略.通过对多种非线性定常系统的多维参数估计和非线性时变 水箱系统的参数与时滞在线联合估计的仿真研究,验证了该方法的可行性、有效性及其一定的 抗噪声能力.     

Simplex filter: A novel heuristic filter for nonlinear systems state estimation

This paper introduces a new filter for nonlinear systems state estimation. The new filter formulates the state estimation problem as a stochastic dynamic optimization problem and utilizes a new stochastic method based on simplex technique to find and track the best estimation. The vertices of the simplex search the state space dynamically in a similar scheme to the optimization algorithm, known as Nelder-Mead simplex. The parameters of the proposed filter are tuned, using an information visualization technique to identify the optimal region of the parameters space. The visualization is performed using the concept of parallel coordinates. The proposed filter is applied to estimate the state of some nonlinear dynamic systems with noisy measurement and its performance is compared with other filters.     

Identification of Neurofuzzy Models Using GTLS Parameter Estimation

In this paper, nonlinear system identification utilizing generalized total least squares (GTLS) methodologies in neurofuzzy systems is addressed. The problem involved with the estimation of the local model parameters of neurofuzzy networks is the presence of noise in measured data. When some or all input channels are subject to noise, the GTLS algorithm yields consistent parameter estimates. In addition to the estimation of the parameters, the main challenge in the design of these local model networks is the determination of the region of validity for the local models. The method presented in this paper is based on an expectation–maximization algorithm that uses a residual from the GTLS parameter estimation for proper partitioning. The performance of the resulting nonlinear model with local parameters estimated by weighted GTLS is a product both of the parameter estimation itself and the associated residual used for the partitioning process. The applicability and benefits of the proposed algorithm are demonstrated by means of illustrative examples and an automotive application.      

Joint state and parameter estimation in particle filtering and stochastic optimization

In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approximation (SPSA) technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibility and efficiency of the proposed algorithm.     

含有有色噪声的非线性分数阶系统自适应扩展卡尔曼滤波器

研究了含有未知参数的情况下，分别含有分数阶有色过程噪声和有色测量噪声的连续时间非线性分数阶系统状态估计问题.采用Grünwald-Letnikov （G-L）差分方法和1阶泰勒展开公式，对描述连续时间非线性分数阶系统的状态方程进行离散化和线性化.构造由状态量、未知参数和分数阶有色噪声的增广向量，设计自适应分数阶扩展卡尔曼滤波算法实现对有色噪声情况下的连续时间非线性分数阶系统的状态和参数的估计.最后，通过分析两个仿真实例，验证了提出算法的有效性.     

Parameter estimation for control systems based on impulse responses

The impulse signal is an instant change signal in very short time. It is widely used in signal processing, electronic technique, communication and system identification. This paper considers the parameter estimation problems for dynamical systems by means of the impulse response measurement data. Since the cost function is highly nonlinear, the nonlinear optimization methods are adopted to derive the parameter estimation algorithms to enhance the estimation accuracy. By using the iterative scheme, the Newton iterative algorithm and the gradient iterative algorithm are proposed for estimating the parameters of dynamical systems. Also, a damping factor is introduced to improve the algorithm stability. Finally, using simulation examples, this paper analyzes and compares the merit and weakness of the proposed algorithms.