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On adaptive control of a partially observed Markov chain

Giovanni Di Masi, Łukasz Stettner (1994)

Applicationes Mathematicae

A control problem for a partially observable Markov chain depending on a parameter with long run average cost is studied. Using uniform ergodicity arguments it is shown that, for values of the parameter varying in a compact set, it is possible to consider only a finite number of nearly optimal controls based on the values of actually computable approximate filters. This leads to an algorithm that guarantees nearly selfoptimizing properties without identifiability conditions. The algorithm is based...

On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve

Darija Marković, Dragan Jukić (2013)

International Journal of Applied Mathematics and Computer Science

The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the parameter estimation approach for the Bass model based on nonlinear weighted least squares fitting of its derivative known as the adoption curve. We show that it is possible that the least squares estimate does not exist. As a main result, two theorems on the existence...

On-line parameter and delay estimation of continuous-time dynamic systems

Janusz Kozłowski, Zdzisław Kowalczuk (2015)

International Journal of Applied Mathematics and Computer Science

The problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous identification of input delay and spectral parameters of the...

Optimal estimator of hypothesis probability for data mining problems with small samples

Andrzej Piegat, Marek Landowski (2012)

International Journal of Applied Mathematics and Computer Science

The paper presents a new (to the best of the authors' knowledge) estimator of probability called the "Epₕ√2 completeness estimator" along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute...

Optimized state estimation for nonlinear dynamical networks subject to fading measurements and stochastic coupling strength: An event-triggered communication mechanism

Chaoqing Jia, Jun Hu, Chongyang Lv, Yujing Shi (2020)

Kybernetika

This paper is concerned with the design of event-based state estimation algorithm for nonlinear complex networks with fading measurements and stochastic coupling strength. The event-based communication protocol is employed to save energy and enhance the network transmission efficiency, where the changeable event-triggered threshold is adopted to adjust the data transmission frequency. The phenomenon of fading measurements is described by a series of random variables obeying certain probability distribution....

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