An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

An exact, closed-form minimum variance filter is designed for a class of discrete time uncertain systems which allows for both multiplicative and additive noise sources. The multiplicative noise model includes a popular class of models (Cox-Ingersoll-Ross type models) in econometrics. The parameters of the system under consideration which describe the state transition are assumed to be subject to stochastic uncertainties. The problem addressed is the design of a filter that minimizes the trace of the estimation error variance. Sensitivity of the new filter to the size of parameter uncertainty, in terms of the variance of parameter perturbations, is also considered. We refer to the new filter as the 'perturbed Kalman filter' (PKF) since it reduces to the traditional (or unperturbed) Kalman filter as the size of stochastic perturbation approaches zero. We also consider a related approximate filtering heuristic for univariate time series and we refer to filter based on this heuristic as approximate perturbed Kalman filter (APKF). We test the performance of our new filters on three simulated numerical examples and compare the results with unperturbed Kalman filter that ignores the uncertainty in the transition equation. Through numerical examples, PKF and APKF are shown to outperform the traditional (or unperturbed) Kalman filter in terms of the size of the estimation error when stochastic uncertainties are present, even when the size of stochastic uncertainty is inaccurately identified

Robust filtering for a class of nonlinear stochastic systems with probability constraints

This paper is concerned with the probability-constrained filtering problem for a class of time-varying nonlinear stochastic systems with estimation error variance constraint. The stochastic nonlinearity considered is quite general that is capable of describing several well-studied stochastic nonlinear systems. The second-order statistics of the noise sequence are unknown but belong to certain known convex set. The purpose of this paper is to design a filter guaranteeing a minimized upper-bound on the estimation error variance. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time. Then, under the probability constraints, a minimax estimation problem is proposed for determining the suboptimal filter structure that minimizes the worst-case performance on the estimation error variance with respect to the uncertain second-order statistics. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed method

Kafka, Jewish Heritage and Hebrew Literature

Razrađujući projekat "Revitalizacija malih jevrejskih opština u Srbiji" urednici „Pinkasa“ su članovima jevrejske zajednice, рге svega u malim opštinama, ponudili kratke, interesantne tekstove sa jevrejskom tematikom, pogodne za čitanje, ali i za organizovanje razgovora u opštinama. Komisija za kulturu i obrazovanje Saveza i Odbor projekta odštampali su tekstove u sveskama (pinkasima) sa temama iz jevrejske istorije (opšte i jugoslovenske), iz umetnosti i nauke, o problemima Holokausta, antisemitizma, jevrejskog identiteta i sl. Jedan od tih tekstova je tekst Geršona Šakeda „Kafka, jevrejsko nasleđe i hebrejska književnost“ u kome analizira Kafkino književno delo i njegov duboki uticaj na hebrejsku književnostElaborating on the project "Revitalization of Small Jewish Communities in Serbia", the editors of “Pinkas“ offered to members of the Jewish community, mostly in small communities, several short, interesting texts on Jewish topics, suitable for reading and organizing conversations in communities. The Commission for Culture and Education of the Federation and the Project Board printed texts in notebooks (pinks) on topics from Jewish history (general and Yugoslav), art and science, problems of the Holocaust, anti-Semitism, Jewish identity, etc. One of these texts is Gershon Shaked's text "Kafka, Jewish Heritage and Hebrew Literature" in which he analyzes Kafka's literary work and its deep impact on Hebrew literature.Ovaj tekst preuzet je iz časopisa za jevrejsku književnost "Mezuza", br. 1/1993. (This text was published in the magazine for Jewish literature "Mezuzah", no. 1/1993).Pinkas 6 - tema: Književnost i jevrejska tradicija (topic: Literature and Jewish tradition)

Advanced topics in control and estimation of state-multiplicative noisy systems

Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems begins with an introduction and extensive literature survey. The text proceeds to cover solutions of measurement-feedback control and state problems and the formulation of the Bounded Real Lemma for both continuous- and discrete-time systems. The continuous-time reduced-order and stochastic-tracking control problems for delayed systems are then treated. Ideas of nonlinear stability are introduced for infinite-horizon systems, again, in both the continuous- and discrete-time cases. The reader is introduced to six practical examples of noisy state-multiplicative control and filtering associated with various fields of control engineering. The book is rounded out by a three-part appendix containing stochastic tools necessary for a proper appreciation of the text: a basic introduction to nonlinear stochastic differential equations and aspects of switched systems and peak to peak  optimal control and filtering. Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems will be of interest to engineers engaged in control systems research and development to graduate students specializing in stochastic control theory and to applied mathematicians interested in control problems. The reader is expected to have some acquaintance with stochastic control theory and state-space-based optimal control theory and methods for linear and nonlinear systems

Stochastic H-infinity tracking with preview for state-multiplicative systems

The problem of finite-horizon H∞ tracking for linear time-varying systems with stochastic parameter uncertainties is investigated. We consider three tracking patterns depending on the nature of the reference signal, i.e., whether it is perfectly known in advance, measured on line or previewed in a fixed time-interval ahead. The stochastic uncertainties appear in both the dynamic and measurement matrices of the system. For each of the above three cases a game theory approach is applied for the state-feedback case where, given a specific reference signal, the controller plays against nature which chooses the initial condition and the energy-bounded disturbance. The problems are solved using an expected value of the standard performance index over the stochastic parameters, where necessary and sufficient conditions are found for the existence of a saddle-point equilibrium. The infinite-horizon time-invariant tracking problem is also solved. The theory developed is demonstrated by a simple tracking example. © 2004 IEEE