scholarly journals Multi-Parameter Estimation of Uncertain Systems Based on the Extended PID Control Method

2021 ◽  
Author(s):  
Jinping Feng ◽  
Wei Wang
Keyword(s):  
Complex System ◽  
Parameter Estimation ◽  
Convergence Analysis ◽  
Control Method ◽  
Estimation Method ◽  
Pid Controllers ◽  
Unknown Parameters ◽  
State Observation ◽  
New States ◽  
Nonlinear Pid Controller

Parameter estimation is an important step in the identification of systems. With the extension of systems, there needs the multi-parameter estimation of systems. The estimation of multi parameters of complex systems based on the extended PID controllers is considered in this chapter. As the related references proved that the integral item of the nonlinear PID controller could deal with the uncertain part of the complex system (which can also be called new stripping principle, simple notes as NSP). Based on this theory, new multi-parameter estimation method is given. Firstly, the unknown parameters are expanded to new states of the system. Two cases, parameters are constant or changing with time, are separately analyzed. In the time-variant case, the unknown parameters are extended to functions which actual forms are uncertain. Secondly the method NSP could be applied to cope with the uncertain part, and then reconstruction state observation to estimate the states. If the states are observed, the unknown parameters are obtained at the same time. Finally the convergence analysis of the error systems and some simulations will be given in this chapter to indicate the effectiveness of the proposed method.

scholarly journals Parameter estimation in a Black Scholes

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 117-122
Author(s):  
Mustafa Bayram ◽  
Buyukoz Orucova ◽  
Tugcem Partal
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Parametric Method ◽  
Estimation Method ◽  
Parametric Estimation ◽  
Likelihood Method ◽  
Observation Data ◽  
Unknown Parameters ◽  
Black Scholes ◽  
Non Parametric

In this paper we discuss parameter estimation in black scholes model. A non-parametric estimation method and well known maximum likelihood estimator are considered. Our aim is to estimate the unknown parameters for stochastic differential equation with discrete time observation data. In simulation study we compare the non-parametric method with maximum likelihood method using stochastic numerical scheme named with Euler Maruyama.

scholarly journals A Well-Designed Parameter Estimation Method for Lifetime Prediction of Deteriorating Systems with Both Smooth Degradation and Abrupt Damage

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Chuanqiang Yu ◽  
Cheng Jiang
Keyword(s):  
Parameter Estimation ◽  
Estimation Method ◽  
Prediction Method ◽  
Estimation Procedure ◽  
Cumulative Distribution ◽  
Lifetime Prediction ◽  
Unknown Parameters ◽  
Lifetime Distributions ◽  
Random Coefficient Regression ◽  
Deteriorating Systems

Deteriorating systems, which are subject to both continuous smooth degradation and additional abrupt damages due to a shock process, can be often encountered in engineering. Modeling the degradation evolution and predicting the lifetime of this kind of systems are both interesting and challenging in practice. In this paper, we model the degradation trajectory of the deteriorating system by a random coefficient regression (RCR) model with positive jumps, where the RCR part is used to model the continuous smooth degradation of the system and the jump part is used to characterize the abrupt damages due to random shocks. Based on a specified threshold level, the probability density function (PDF) and cumulative distribution function (CDF) of the lifetime can be derived analytically. The unknown parameters associated with the derived lifetime distributions can be estimated via a well-designed parameter estimation procedure on the basis of the available degradation recordings of the deteriorating systems. An illustrative example is finally provided to demonstrate the implementation and superiority of the newly proposed lifetime prediction method. The experimental results reveal that our proposed lifetime prediction method with the dedicated parameter estimation strategy can get more accurate lifetime predictions than the rival model in literature.

Parameter estimation and synchronization of hyper chaotic Lu system with disturbance input and uncertainty using two under-actuated control signals

2018 ◽  
Vol 41 (6) ◽  
pp. 1729-1739
Author(s):  
Alireza Sabaghian ◽  
Saeed Balochian
Keyword(s):  
Parameter Estimation ◽  
Lyapunov Stability ◽  
Control Method ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode Controller ◽  
Control Signals ◽  
Stability Method ◽  
Measure Of Performance

In this paper, synchronization of two hyper chaotic Lu systems with unknown factors, such as uncertainty and disturbance, and less control signals with respect to system’s dimensions by applying an adaptive sliding mode controller is presented. In this research, firstly, an integral sliding mode controller is designed for synchronization of two hyper chaotic Lu systems with known parameters. Secondly, a controller is used to synchronize two hyper chaotic Lu systems with unknown parameters; in this case, unknown parameters are estimated using an adaptive rule. As a measure of performance, stability of the proposed control method is proved using the Lyapunov stability method. Numerical simulations validate the stabilization and synchronization.

scholarly journals Novel Optimization-Based Parameter Estimation Method for the Bass Diffusion Model

SAGE Open ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 215824402110269
Author(s):  
Lang Liang
Keyword(s):  
Parameter Estimation ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Reference Value ◽  
Diffusion Problem ◽  
Bass Model ◽  
Weighted Least Squares Method ◽  
Estimated Parameters ◽  
Bass Diffusion Model

The Bass model is the most popular model for forecasting the diffusion process of a new product. However, the controlling parameters in it are unknown in practice and need to be determined in advance. Currently, the estimation of the controlling parameters has been approached by various techniques. In this case, a novel optimization-based parameter estimation (OPE) method for the Bass model is proposed in the theoretical framework of system dynamics ( SD). To do this, the SD model of the Bass differential equation is first established and then the corresponding optimization mathematical model is formulated by introducing the controlling parameters as design variable and the discrepancy of the adopter function to the reference value as objective function. Using the VENSIM software, the present SD optimization model is solved, and its effectiveness and accuracy are demonstrated by two examples: one involves the exact solution and another is related to the actual user diffusion problem from Chinese Mobile. The results show that the present OPE method can produce higher predicting accuracy of the controlling parameters than the nonlinear weighted least squares method and the genetic algorithms. Moreover, the reliability interval of the estimated parameters and the goodness of fitting of the optimal results are given as well to further demonstrate the accuracy of the present OPE method.

Topology detection of a distribution network based on adaptive state observer

2021 ◽  
pp. 1-9
Author(s):  
Yong Xiao ◽  
Yonggang Zeng ◽  
Yun Zhao ◽  
Yuxin Lu ◽  
Weibin Lin
Keyword(s):  
Smart Grid ◽  
Distribution Network ◽  
Detection Algorithm ◽  
State Observer ◽  
Matlab Simulation ◽  
Unknown Parameters ◽  
State Observation ◽  
Observation Network ◽  
Topology Information ◽  
Adaptive State Observer

The traditional distribution network lacks real-time topology information, which makes the implementation of smart grid complicated. The smart grid needs to monitor and dispatch the grid to maintain the economic and safe operation of the system. In this paper, we propose a topology detection algorithm of the distribution network based on adaptive state observer. Based on the transient dynamic model of the distribution network, the line states of the distribution network are regarded as unknown parameters, a virtual adaptive state observation network is built, and the topology can be inferred by the changes of adaptive state parameters. Finally, the effectiveness of our algorithm is verified by the MATLAB simulation experiments.

scholarly journals MLE-Based Parameter Estimation for Four-Parameter Exponential Gamma Distribution and Asymptotic Variance of Its Quantiles

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2092
Author(s):  
Songbai Song ◽  
Yan Kang ◽  
Xiaoyan Song ◽  
Vijay P. Singh
Keyword(s):  
Parameter Estimation ◽  
Confidence Intervals ◽  
Asymptotic Variance ◽  
Information Matrix ◽  
Estimation Method ◽  
Flood Frequency Analysis ◽  
Annual Precipitation ◽  
Precipitation Data ◽  
Marquardt Algorithm ◽  
Design Values

The choice of a probability distribution function and confidence interval of estimated design values have long been of interest in flood frequency analysis. Although the four-parameter exponential gamma (FPEG) distribution has been developed for application in hydrology, its maximum likelihood estimation (MLE)-based parameter estimation method and asymptotic variance of its quantiles have not been well documented. In this study, the MLE method was used to estimate the parameters and confidence intervals of quantiles of the FPEG distribution. This method entails parameter estimation and asymptotic variances of quantile estimators. The parameter estimation consisted of a set of four equations which, after algebraic simplification, were solved using a three dimensional Levenberg-Marquardt algorithm. Based on sample information matrix and Fisher’s expected information matrix, derivatives of the design quantile with respect to the parameters were derived. The method of estimation was applied to annual precipitation data from the Weihe watershed, China and confidence intervals for quantiles were determined. Results showed that the FPEG was a good candidate to model annual precipitation data and can provide guidance for estimating design values

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