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LARGE DEVIATIONS ANALYSIS OF SOME recursive algorithms WITH STATE DEPENDENT NOISE

ANNALS OF PROBABILITY 1988年第4期16卷 1509-1536页

作者： DUPUIS, P BOSTON UNIV BOSTONMA 02215 UNIV MINNESOTA IMAMINNEAPOLISMN 55455

Consider the recursive, stochastic algorithm Xn+1ε=Xnε+εb(Xnε,ξn), where {ξn} is a random process and Xnε lives in Rd. algorithms of this type arise frequently in applications in control and communications, as well as elsewhere. In the study of the important long term behavior of such recursive algorithms the "large deviations" behavior of the system, which describes the asymptotics of the order 1 deviations of the system from its "mean" trajectory as ε tends to 0, plays a central role. Typical systems arising in communication theory and control often use complicated forcing terms involving correlated and state dependent noises and forcing terms with discontinuities. This paper presents a general approach for proving large deviations type theorems for such systems. The problem of proving such a theorem is considered first for the general case of a stochastic process with Lipschitz continuous sample paths. The assumptions are stated in terms of the conditional distribution of time increments of the process. After giving the proof in this general framework, we give several examples (in both continuous and discrete time) of driving terms that satisfy the hypotheses. The results are subsequently extended to a "projected" version of the discrete time model. The paper concludes with an application of the results to an automatic routing mechanism.

关键词： 60F10 62L20 asymptotic analysis large deviations recursive algorithms state dependent noises

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STOCHASTIC-APPROXIMATION AND LARGE DEVIATIONS - UPPER-BOUNDS AND W.P.1 CONVERGENCE

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1989年第5期27卷 1108-1135页

作者： DUPUIS, P KUSHNER, HJ BROWN UNIV LEFSCHENCE CTR DYNAM SYSTDIV APPL MATHPROVIDENCERI 02912

With probability one convergence results are obtained for stochastic recursive approximation algorithms under very general conditions. The gain sequence $\{ a_n \} $ can go to zero very slowly and state-dependent noise, discontinuous dynamical equations, and the projected or constrained algorithm are all treated. The basic technique is the theory of large deviations. Prior results obtained via this theory are extended in many directions. Let $\dot x = \bar b(x)$ denote the “mean” equation for the algorithm, let $\delta > 0$ be given, and let $G(\theta )$ be a neighborhood of a stable point $\theta $ of that ordinary differential equation. Then, asymptotic upper bounds to $a_N \log P\{ X_n \notin G(\theta ),n \geqq N\mid | {X_N - \theta } | \leqq \delta \} $, are obtained. These are often more informative than the usual classical rate of convergence results (that use a “local linearization”) and, furthermore, are obtained for the constrained and nonsmooth cases, for which there are no “rate of convergence” results. The methods are also used to extend currently available upper bounds for algorithms with constant gains, with simpler proofs.

关键词： 60F10 62L20 93E10 93E12 stochastic approximation large deviations recursive algorithms errors for tracking systems

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ROUND-OFF ERROR PROPAGATION IN 4 GENERALLY-APPLICABLE, recursive, LEAST-SQUARES ESTIMATION SCHEMES

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AUTOMATICA 1989年第3期25卷 437-444页

作者： VERHAEGEN, MH Department of Electrical Engineering Control Laboratory Delft University of Technology NL-2628 CD Delft P.O. Box 5031 Netherlands

The numerical robustness of four generally-applicable, recursive, least-squares estimation schemes is analysed by means of a theoretical round-off propagation study. This study highlights a number of practical, interesting insights into the widely-used recursive least-squares schemes. These insights have been confirmed in an experimental verification study.

关键词： computer simulation least-squares estimation, numerical analysis recursive algorithms

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AN FFT ALGORITHM BASED FAST ALGORITHM FOR ARBITRARY POLYNOMIAL TRANSFORMATION

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IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING 1989年第10期37卷 1612-1614页

作者： KRISHNA, H Department of Electrical and Computer Engineering Syracuse University Syracuse NY USA

A fast algorithm for the arbitrary polynomial transformation is described. This algorithm is based on the fast Fourier transform (FFT) algorithm and reduces the computational complexity of a recently proposed recursiv... 详细信息

关键词： Arbitrary recursive algorithms complexity classes Fasting FFT algorithm algorithms Polynomial

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algorithms for Estimation of the Assemblywise Power Distribution in WWER Type Reactors

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IFAC Proceedings Volumes 1989年第16期22卷 333-336页

作者： R. Tsvetanov F.F. Pashchenko N.P. Kolev Institute of Control Science Profsoyuznaia 65 Moscow 117342 USSR Institute for Nuclear Research and Nuclear Energy baul. Lenin 12 Sofia 1784 Bulgaria

Two efficient algorithms for estimation of the assemblywise Power distribution on WWER type reactors are presented. The algorithms combine reference code pre-calculations with aposteriori corrections based on temperature measurements at the reactor core outlet. An adaptive multiplicative correction function and a quadratic performance criterion are used. The problem for estimation of the unknown coefficients in the correction function is solved in two ways: (a) using a recursive stochastic approximation algorithm, and (b) by a least squares algorithm with singular value decomposition techniques. The two algorithms were run with sets of measured data in order to provide results for a comprehensive comparison of their accuracy, efficiency and stability with respect to measurement errors. One of the presented procedures is implemented in a computerized power shape monitoring subsystem at the Kozlodui NPP.

关键词： Nuclear reactors power distribution estimation computer evaluation recursive algorithms stochastic approcimations least-squares approximations numerical methods

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Identifier-Based Adaptive Monitoring and Control for Stream-Flow Transportation Systems

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IFAC Proceedings Volumes 1989年第16期22卷 209-213页

作者： Yu.V. Panich M.L. Trachevsky VIASM Institute 13 Chekistov ul Leningrad 198206 USSR

The problem under discussion is synthesis of adaptive monitoring and control systems for stream-flow transportation complexes comprising intermediate and blending storages, with drifting parameters of monitored objects and with no direct storage stock-taking facilities. The problem can be handled by finding balanced flow and store estimates that would comply with control-imposed physical constraints on variable states of intermediate storages. An independent identification of objects is shown to result in divergence of the estimates in the state space. Co-identification algorithms are described which, using a priori information on material balance conditions, warrant both a good compliance with constraints on variable states and a faster identification of parameters in the space. The allowance for the constraints is found to be equivalent to having extra monitoring channels. An embodiment of this approach in a centralized material- flow monitoring system of an ore-dressing plant is described.

关键词： Materials handling intermediate storage closed-loop systems models identification recursive algorithms adaptive systems

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Analysis of Robust recursive Identification algorithms

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IFAC Proceedings Volumes 1987年第5期20卷 321-326页

作者： V.Z. Filipovic B.D. Kovacevic Faculty of Electrical Engineering University of Belgrade Belgrade Yugoslavia

The problem of recursive robust identification of linear discrete-time dynamic stochastic systems is discussed. Supposing approximately Gaussian system disturbance samples, a general form of robustified recursive identification algorithms of stochastic approximation type, characterized by an adequate nonlinear residual transformation, is defined. In order to improve the convergence rate, especially on short data sequences, the weighting matrix of the algorithm is derived by performing step-by-step optimization of a predefined empirical criterion. The convergence of the estimates w.p.l. is established theoretically by using martingale theory. The theoretical results are followed by extensive Monte Carlo simulation results, providing a basis for making a precise judgement of real practical robustness of the algorithms. Important relationships between parameters describing the algorithms are pointed out.

关键词： Identification recursive algorithms robustness sensitivity simulation

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SYMBOL ERROR RATE CURVES FOR M-QAM SIGNALS WITH MULTIPLE COCHANNEL INTERFERERS

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IEEE TRANSACTIONS ON COMMUNICATIONS 1988年第8期36卷 980-983页

作者： COCO, RA AT&T Bell Laboratories MA USA

A recursive algorithm for determining the probability of symbol error in an M-QAM system, subject to multiple-cochannel interferers, is presented. In particular, a recursive formula is derived for determining the symbol-error-rate (SER) of an M-QAM system subject to both multiple-sinusoidal and similar, independent QAM interferers. The result is expected to prove useful in the analysis of such systems exposed to ever-increasing interference.

关键词： recurrence formula recursive algorithms Quadrature amplitude modulation Analysis systems Curves SAFETY EVALUATION REPORT signals

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recursive BAYESIAN-ESTIMATION USING PIECE-WISE CONSTANT APPROXIMATIONS

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AUTOMATICA 1988年第6期24卷 789-801页

作者： KRAMER, SC SORENSON, HW USAF WASHINGTONDC 20330

In Bayesian estimation, the objective is to calculate the complete density function for an unknown quantity conditioned on noisy observations of that quantity. This work considers recursive estimation of a nonlinear discrete-time system state using successive observations. The formal recursion for the density function is easily written, but generally there is no closed form solution. The numerical solution proposed here is obtained by modifying the recursion and using a simple piece-wise constant approximation to the density functions. The approach also allows detailed analysis of error propagation through the algorithm, yielding a bound on the maximum error growth, and a characterization of the situations with potential for large errors. The stability of the algorithm is demonstrated by comparing its long-term performance to a Kalman filter for a linear system with Gaussian noises. Comparison to the point mass algorithm shows improved estimation accuracy, and, for moderately dense grids, faster computation. As an example, the algorithm is applied to a system identification problem, and the results compared to a popular second order minimum variance estimator. The optimal estimate derived from the approximate density is seen to be far superior.

关键词： Bayes methods discrete-time systems estimation nonlinear systems parameter estimation recursive algorithms state estimation stochastic systems

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NORMAL COORDINATE EXPANSION OF THE WESS-ZUMINO-WITTEN MODEL

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EUROPHYSICS LETTERS 1988年第2期6卷 113-117页

作者： XI, ZM Center of Theoretical Physics CCAST (World Laboratory) Institute of Theoretical Physics Academia Sinica - P.O. Box 2735 Beijing China

The recursive algorithm of the normal coordinate expansion of the nonlinear sigma-model of Mukhi is extended. A simple background field expansion for the Wess-Zumino-Witten nonlinear sigma-model is presented. The general structure of itsn-th order term in the expansion is explicitly given. It is shown that this expansion is equivalent to the usual background field expansion in the matrix form of the chiral model.

关键词： normal coordinates recursive algorithms general structure Sigma model Expansion Equivalent

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