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State estimation for stochastic polynomial systems with switching in the state equation

TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2018年第9期40卷 2732-2739页

作者： Hernandez-Gonzalez, Miguel Basin, Michael V. Autonomous Univ Nuevo Leon Dept Phys & Math Sci Cd Univ San Nicolas De Los Garza 66455 Nuevo Leon Mexico ITMO Univ Int Sci Lab Integrated Syst Orientat & Nav St Petersburg Russia

The problem of designing a mean-square filter has been studied for stochastic polynomial systems, where the state equation switches between two different nonlinear functions, over linear observations. A switching signal depends on a random variable modelled as a Bernoulli distributed sequence that takes the quantities of zero and one. The differential equations for the state estimate and the error covariance matrix are obtained in a closed form by expressing the conditional expectation of polynomial terms as functions of the estimate and covariance matrix. Finite-dimensional filtering equations are obtained for a particular case of a third-degree polynomial system. Numerical simulations are carried out in two cases of switching between different linear and second degree polynomial functions.

关键词： Filtering equations polynomial functions hybrid systems

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SCALING THEOREMS FOR ZERO-CROSSINGS

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1990年第1期12卷 46-54页

作者： WU, L XIE, ZH Dept. of Comput. Sci. Fudan Univ. Shanghai China

Two scaling theorems are given. Instead of delta functions, polynomial functions are used as input. The advantages are twofold: the smoothness conditions on kernels are not required, so that kernels of the form e/sup -k mod X mod / can be included; the proofs are based on calculus completely and so can be more easily understood.","doi":"10.1109/34.41383","publicationTitle":"IEEE Transactions on Pattern Analysis and Machine Intelligence","startPage":"46","endPage":"54","rightsLink":"http://***/AppDispatchServlet?publisherName=ieee&publication=0162-8828&title=Scaling+theorems+for+zero-crossings&isbn=&publicationDate=Jan.+1990&author=+Lide+Wu&ContentID=10.1109/34.41383&orderBeanReset=true&startPage=46&endPage=54&volumeNum=12&issueNum=1","displayPublicationTitle":"IEEE Transactions on Pattern Analysis and Machine Intelligence","pdfPath":"/iel1/34/1584/***","keywords":[{"type":"IEEE Keywords","kwd":["Kernel","polynomials","Hydrogen","Calculus","Computer science","Filters","Computer vision","Laplace equations","Image edge detection","Detectors"]},{"type":"INSPEC: Controlled Indexing","kwd":["polynomials","pattern recognition"]},{"type":"INSPEC: Non-Controlled Indexing","kwd":["smoothness conditions","pattern recognition","scaling theorems","zero-crossings","polynomial functions"]}],"allowComments":false,"pubLink":"/xpl/***?punumber=34","issueLink":"/xpl/***?isnumber=1584","standardTitle":"Scaling theorems for zero-crossings

关键词： Kernel polynomials Hydrogen Calculus Computer science Filters Computer vision Laplace equations Image edge detection Detectors INSPEC: Controlled Indexing polynomials pattern recognition INSPEC: Non-Controlled Indexing smoothness conditions pattern recognition scaling theorems zero-crossings polynomial functions

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Optimal dynamic-inversion-based control of an overhead crane

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IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS 2002年第5期149卷 405-411页

作者： Piazzi, A Visioli, A Univ Parma Dipartimento Ingn Informaz I-43100 Parma Italy Univ Brescia Dipartimento Elettron & Automaz I-25121 Brescia Italy

A methodology is proposed to control the transient sway and residual oscillation of a payload carried by an overhead crane. The design approach is based on a linearised model of the crane and consists of dampening the linearised system by an observer-based controller and applying a dynamic inversion procedure in order to assure a predetermined oscillation free polynomial motion law for the payload. polynomial functions are adopted in order to guarantee that the input function has a continuous derivative of an arbitrary order. Moreover, the motion time can be minimised, taking into account constraints on the actuators, by means of a simple bisection algorithm. Parameter uncertainties are taken into account during the whole design procedure. Simulation results, based on a nonlinear crane model, show how the method is also effective when the payload is hoisted or lowered during the motion, and when friction effects are considered.

关键词： parameter uncertainties functions nonlinear systems design approach motion control Control applications to materials handling friction polynomial functions state feedback feedforward cranes transient sway Materials handling equipment residual oscillation Materials handling and distribution optimal control Optimal control Nonlinear control systems Algebra nonlinear crane model polynomials optimal dynamic-inversion-based control control system synthesis bisection algorithm Control system analysis and synthesis methods friction effects overhead crane payload observer-based controller predetermined oscillation free polynomial motion law Spatial variables control linearised model

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A maximum A posteriori approach to speaker adaptation using the trended hidden Markov model

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IEEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING 2001年第5期9卷 549-557页

作者： Chengalvarayan, R Deng, L Lucent Technol Inc Lucent Speech Solut Naperville IL 60566 USA Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

A formulation of the maximum a posteriori (MAP) approach to speaker adaptation is presented with use of the trended or nonstationary-state hidden Markov model (HMM), where the Gaussian means in each HMM state are characterized by time-varying polynomial trend functions of the state sojourn time. Assuming uncorrelatedness among the polynomial coefficients in the trend functions, we have obtained analytical results for the MAP estimates of the parameters including time-varying means and time-invariant precisions. We have implemented a speech recognizer based on these results in speaker adaptation experiments using the TI46 corpora, The experimental evaluation demonstrates that the trended HMM, with use of either the linear or the quadratic polynomial trend function, consistently outperforms the conventional, stationary-state HMM, The evaluation also shows that the unadapted, speaker-independent models are outperformed by the models adapted by the MAP procedure under supervision with as few as a single adaptation token. Further, adaptation of polynomial coefficients alone is shown to be better than adapting both polynomial coefficients and precision matrices when fewer than four adaptation tokens are used, while the reverse is found with a greater number of adaptation tokens.

关键词： adaptation hidden Markov models MAP estimation polynomial functions speech recognition

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A Different Version of Flett's Mean Value Theorem and an Associated Functional Equation

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Acta Mathematica Sinica,English Series 2004年第6期20卷 1073-1078页

作者： Thomas RIEDEL Maciej SABLIK Department of Mathematics University of Louisville Institute of Mathematics Silesian University

In this paper we present a mean value theorem derived from Flett's mean value theorem. It turns out that cubic polynomials have the midpoint of the interval as their mean value *** answer what class of functions have this property,we consider a functional equation associated with this mean value *** equation is then solved in a general setting on abelian groups.

关键词： Flett's mean value theorem Functional equations polynomial functions

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On a functional equation connected to Hermite quadrature rule

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2014年第2期414卷 632-640页

作者： Koclega-Kulpa, Barbara Szostok, Tomasz Silesian Univ Inst Math PL-40007 Katowice Poland

In this paper we deal with the functional equation F(y) - F(x) = (y - x)[alpha f (x) + beta f (x + y/2) +alpha f(y)] + (y - x)(2) [g(y) - g(x), which is connected to Hermite quadrature rule. It is easy to note that particular cases of this equation generalize many well known functional equations connected to quadrature rules and mean value theorems. Thus the set of solutions is too complicated to be described completely and therefore we prove that (under some assumptions) all solutions of the above equation must be polynomials. We obtain the aforementioned result using a lemma proved by M. Sablik, however this lemma works only in case beta not equal 0. Taking beta = 0, we obtain the following equation F(y) - F(x) = (y - x)[f(x) + f (y)] + (y - x)(2) [g(y) - g (x)], which is also solved in the paper. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Functional equations Approximate integration polynomial functions Quadrature rules

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polynomial clones on groups of order pq

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ACTA MATHEMATICA HUNGARICA 2007年第3期114卷 267-285页

作者： Aichinger, E. Mayr, P. Johannes Kepler Univ Linz Inst Algebra A-4040 Linz Austria

For two distinct primes p, q, we describe those clones on a set of size pq that contain a given group operation and all constant operations. We show that each such clone is determined by congruences and commutator rel... 详细信息

关键词： Mal'cev clones polynomial functions polynomial completeness commutator theory

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The ring of polyfunctions over Z/nZ

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COMMUNICATIONS IN ALGEBRA 2023年第1期51卷 116-134页

作者： Specker, Ernst Hungerbuhler, Norbert Wasem, Micha Swiss Fed Inst Technol Dept Math Ramistr 101 CH-8092 Zurich Switzerland HES SO Univ Appl Sci & Arts Western Switzerland HTA Freiburg Fribourg Switzerland UniDistance Suisse Brig Switzerland

We study the ring of polyfunctions over Z/nZ. The ring of polyfunctions over a commutative ring R with unit element is the ring of functions f : R -> R which admit a polynomial representative p is an element of R[x] in the sense that f(x) = p(x) for all x is an element of R. This allows to define a ring invariant s which associates to a commutative ring R with unit element a value in N boolean OR{infinity}. The function s generalizes the number theoretic Smarandache function. For the ring R = Z/nZ we provide a unique representation of polynomials which vanish as a function. This yields a new formula for the number Psi(n) of polyfunctions over Z/nZ. We also investigate algebraic properties of the ring of polyfunctions over Z/nZ. In particular, we identify the additive subgroup of the ring and the ring structure itself. Moreover we derive formulas for the size of the ring of polyfunctions in several variables over Z/nZ, and we compute the number of polyfunctions which are units of the ring.

关键词： polynomial functions ring invariant Smarandache function

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Vanishing cycles of pencils of hypersurfaces

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TOPOLOGY 2004年第3期43卷 619-633页

作者： Tibar, M Univ Sci & Tech Lille Flandres Artois F-59655 Villeneuve Dascq France

We prove an extended Lefschetz principle for a large class of pencils of hypersurfaces having isolated singularities, possibly in the axis, and show that the module of vanishing cycles is generated by the images of ce... 详细信息

关键词： vanishing cycles nongeneric pencils second Lefschetz theorem monodromy variation map topology of polynomial functions

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On quadrature means

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AEQUATIONES MATHEMATICAE 2023年第5-6期97卷 935-949页

作者： Szostok, Tomasz Univ Silesiaia Inst Math Bankowa 14 PL-40007 Katowice Poland

We observe that every quadrature of numerical integration together with a strictly increasing and continuous function generates a mean and then we study this family of means. We characterize the functions which generate weighted arithmetic means in this way and we show how to obtain comparison type theorems for means generated by different quadratures.

关键词： Means polynomial functions Convex functions Convex functions of higher orders Stochastic orderings

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