A Bayes Estimator of Parameters of Nonlinear Dynamic Systems
نویسنده
چکیده
A new multipolynomial approximations algorithm the MPA algorithm is proposed for estimating the state vector θ of virtually any dynamical evolutionary system. The input of the algorithm consists of discrete-time observations Y . An adjustment of the algorithm is required to the generation of arrays of random sequences of state vectors and observations scalars corresponding to a given sequence of time instants. The distributions of the random factors vectors of the initial states and random perturbations of the system, scalars of random observational errors can be arbitrary but have to be prescribed beforehand. The output of the algorithm is a vector polynomial series with respect to products of nonnegative integer powers of the results of real observations or some functions of these results. The sum of the powers does not exceed some given integer d. The series is a vector polynomial approximation of the vector E θ | Y , which is the conditional expectation of the vector under evaluation or given functions of the components of that vector . The vector coefficients of the polynomial series are constructed in such a way that the approximation errors uniformly tend to zero as the integer d increases. These coefficients are found by the Monte-Carlo method and a process of recurrent calculations that do not require matrix inversion.
منابع مشابه
Classic and Bayes Shrinkage Estimation in Rayleigh Distribution Using a Point Guess Based on Censored Data
Introduction In classical methods of statistics, the parameter of interest is estimated based on a random sample using natural estimators such as maximum likelihood or unbiased estimators (sample information). In practice, the researcher has a prior information about the parameter in the form of a point guess value. Information in the guess value is called as nonsample information. Thomp...
متن کاملAdaptive neural control of nonlinear fractional order multi- agent systems in the presence of error constraintion
In this paper, the problem of fractional order multi-agent tracking control problem is considered. External disturbances, uncertainties, error constraints, transient response suitability and desirable response tracking problems are the challenges in this study. Because of these problems and challenges, an adaptive control and neural estimator approaches are used in this study. In the first part...
متن کاملDevelopment of a Robust Observer for General Form Nonlinear System: Theory, Design and Implementation
The problem of observer design for nonlinear systems has got great attention in the recent literature. The nonlinear observer has been a topic of interest in control theory. In this research, a modified robust sliding-mode observer (SMO) is designed to accurately estimate the state variables of nonlinear systems in the presence of disturbances and model uncertainties. The observer has a simple ...
متن کاملTruncated Linear Minimax Estimator of a Power of the Scale Parameter in a Lower- Bounded Parameter Space
Minimax estimation problems with restricted parameter space reached increasing interest within the last two decades Some authors derived minimax and admissible estimators of bounded parameters under squared error loss and scale invariant squared error loss In some truncated estimation problems the most natural estimator to be considered is the truncated version of a classic...
متن کاملPotentials of Evolving Linear Models in Tracking Control Design for Nonlinear Variable Structure Systems
Evolving models have found applications in many real world systems. In this paper, potentials of the Evolving Linear Models (ELMs) in tracking control design for nonlinear variable structure systems are introduced. At first, an ELM is introduced as a dynamic single input, single output (SISO) linear model whose parameters as well as dynamic orders of input and output signals can change through ...
متن کاملMinimax Estimator of a Lower Bounded Parameter of a Discrete Distribution under a Squared Log Error Loss Function
The problem of estimating the parameter ?, when it is restricted to an interval of the form , in a class of discrete distributions, including Binomial Negative Binomial discrete Weibull and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function....
متن کامل