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SQUARE ROOT FILTERING VIA COVARIANCE AND INFORMATION EIGENFACTORS

AUTOMATICA 1986年第5期22卷 599-604页

作者： OSHMAN, Y BARITZHACK, IY Department of Aeronautical Engineering Technion - Israel Institute of Technology Haifa 32000 Israel

Two new square root Kalman filtering algorithms are presented. Both algorithms are based on the spectral V − Λ of the covariance matrix where V is the matrix whose columns are the eigenvectors of the covariance and Λ is the diagonal matrix of its eigenvalues. The algorithms use the covariance mode in the time propagation stage and the information mode in the measurement update stage. This switch between modes, which is trivial in the V − Λ representation, increases the efficiency of the algorithms. In the first algorithm, which is a continuous/discrete one, the V and Λ 1 2 matrices are propagated in time in a continuous manner, while the measurement update is a discrete time procedure. In the second algorithm, which is a discrete/discrete one, the time propagation of the V − Λ 1 2 factors is performed in discrete time too, using a procedure which is similar to the one used for the discrete measurement update. The discrete propagation and the measurement update are based on singular value decomposition algorithms. The square root nature of the algorithms is demonstrated numerically through a typical example. While promising all the virtues of square root routines, the V − Λ filters are also characterized by their ability to exhibit singularities as they occur.

关键词： (Square root filtering) decomposition eigenvalues filtering Kalman filters numerical methods recursive algorithms signal processing state estimation

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ASYMPTOTICALLY OPTIMUM recursive PREDICTION ERROR METHODS IN ADAPTIVE ESTIMATION AND CONTROL

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AUTOMATICA 1986年第2期22卷 237-240页

作者： MOORE, JB BOEL, RK Department of Systems Engineering Research School of Physical Sciences Australian National University Canberra ACT 2601 Australia Visiting Research Fellow (NFWO) Department of Systems Engineering Research School of Physical Sciences Australian National University on leave from an NFWO (Belgium National Foundation for Scientific Research) Research Fellow position at the Rijksuniversiteit Gent Belgium

The challenge taken up in this paper is to devise a parameter identification algorithm for linear, discrete-time, stochastic plants which exploits the strengths of both the extended least squares (ELS) and the recursive prediction error (RPE) parameter estimation methods. The focus is on adaptive control of parameterized state space models which exploit a priori plant information in that the unknown parameter vector θ r is of lower dimension than that for a corresponding input-output model parameterized by θ. A triple parameter estimation scheme consisting of ELS, RPE and a hybrid of the two, denoted HPE, is proposed. The purpose of the HPE scheme is to permit information flow from the ELS to RPE algorithms so as to effectively project RPE into a stability domain, and to have it avoid local prediction error index minima that are not the global minimum.

关键词： Adaptive control adaptive systems control system design parallel processing parameter estimation recursive algorithms

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STOCHASTIC APPROXIMATIONS VIA LARGE DEVIATIONS - ASYMPTOTIC PROPERTIES

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1985年第5期23卷 675-696页

作者： DUPUIS, P KUSHNER, HJ Brown Univ Div of Applied Mathematics Providence RI USA Brown Univ Div of Applied Mathematics Providence RI USA

Asymptotic properties of Robbins–Munro and Kiefer–Wolfowitz type stochastic approximation algorithms are obtained via the theory of large deviations. The conditions are weak and can even yield w.p.l. convergence results. The probability of escape of the iterates from a neighborhood of a stable point of the algorithm is estimated and shown to be considerably smaller than suggested by the classical “asymptotic normality of local normalized errors” method of getting the asymptotic properties. The escape probabilities are a natural quantity of interest. In many applications, they are more useful than the “local normalized mean square errors.” Other large deviations estimates are also obtained. Typically, if ${{a_n = 1} / {n^\rho }}$, $\rho \leqq 1$, then the probability of escape from a neighborhood of a stable point in some (normalized) time interval $[n,m]:\sum_n^m {a_i \sim T} $ is $\exp - n^\rho V_\rho $, where $V_\rho $ does not depend on $\rho $ for $\rho < 1$ and is the solution to an optimal control problem. If the noise is Gaussian, then the optimal control problem is relatively easy. Under quite broad conditions, in the Kiefer–Wolfowitz case the control problem has the Gaussian form, whether or not the noise is Gaussian. The techniques are expected to be quite useful in the analysis of the asymptotic properties of recursive algorithms generally.

关键词： stochastic approximation large deviations recursive algorithms asymptotic properties

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TRACKING ERROR-BOUNDS OF ADAPTIVE NONSTATIONARY FILTERING

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AUTOMATICA 1985年第3期21卷 293-302页

作者： EWEDA, E MACCHI, O CNRS ECOLE SUPER ELECTSIGNAUX & SYST LABF-91190 GIF SUR YVETTEFRANCE

Adaptive filtering with error gradient algorithm and constant step-size is analyzed for a deterministic time variable optimum filtering vector. The unrealistic assumption of independent observations is replaced by a bounded memory model, largely justifiable in applications. Then the mean square tracking deviation (MSD) between the optimum vector and the algorithm output is proved to include two contributions; the stationary mode error, characteristic of convergence accuracy, which is proportional to the step-size; and the transient mode error, reflecting the rapidity of tracking, which is proportional to the squared ratio of the maximum optimum estimator increment to the step-size. This result agrees with the common intuition that there exists an optimum step-size which compromises between convergence accuracy and tracking speed.

关键词： Adaptive systems discrete time systems filtering least-squares estimation linear systems random processes recursive algorithms time-varying systems

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OPTIMIZATION WITH RESPECT TO COVARIANCE SEQUENCE PARAMETERS

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AUTOMATICA 1985年第6期21卷 671-675页

作者： STOICA, P SODERSTROM, T UNIV UPPSALA INST TECHNOLDEPT AUTOMAT CONTROL & SYST ANALS-75121 UPPSALASWEDEN

A general problem involving optimization of a covariance sequence is considered in the paper. One difficulty with this class of problems is to ensure that the covariance sequence is nonnegative definite (in other words, realizable). It is suggested that this difficulty can be overcome by reformulating the optimization problem in terms of the partial autocorrelation coefficients (PAC). One need only constrain these coefficients to lie in the range (−1, 1) to guarantee that the corresponding covariance sequence is nonnegative definite. The synthesis of a signal realizing the optimizing covariance sequence is also discussed. Special emphasis is given to the case when some of the PACs are either +1 or −1.

关键词： Correlation methods estimation optimization recursive algorithms signal processing time-series analysis

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ON 2ND-ORDER FILTER PERFORMANCE

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AUTOMATICA 1985年第3期21卷 333-336页

作者： WILLMAN, WW Research Department Naval Weapons Center China Lake CA 93555 United States

Monte Carlo simulation is used to compare the numerical performance of a second-order filtering algorithm with those of two previously tested filters in a well-known nonlinear state estimation problem.

关键词： Bayes methods filtering nonlinear filtering parameter estimation perturbation techniques recursive algorithms sampled data systems state estimation stochastic systems

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Application of the Stochastic Gradient Method to the Control of a Non-Linear Process Modelled as a Markov Chain

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IFAC Proceedings Volumes 1985年第5期18卷 357-362页

作者： A. Majdoul L.E.E.S.A. Faculte de Science B.P. 1014 Rabat Morocco

Computing the control law for non-linear systems can be facilitated by using a stochastic automaton model. The automaton adapts i5 policy by means of a stochastic gradient algorithm, that depends on the estimation of ... 详细信息

关键词： Non-linear process markov chain learning automata recursive algorithms

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A Multipredictor-Based LQ Self-Tuning Controller

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IFAC Proceedings Volumes 1985年第5期18卷 137-141页

作者： J.M. Lemos E. Mosca Centro de Anàlise e Processamento de Sinais Universidade Técnica de Lisboa Av. Rovisco Pais 1000 Lisboa Portugal Dipartimento di Sistemi e Informatica Università di Firenze Via S. Marta 3 50139 Firenze Italy

The problem of controlling a plant with unknown and slowly time-varying para meters is considered. In order to make the resulting adaptive controller robust against model mismatching, future bahaviour of the plant is not described by a single predictive model but by a number of different predictive models whose parameters are independently estimated. Attention is devoted to developing recursive least-squares (RLS) estimators consisting of UD covariance filters or square root information filters that, by exploiting the relationship among different regressors, keep the overall numerical burden as small as possible

关键词： Adaptive control self-tuning controllers recursive algorithms linear optimal regulators least-squares estimation

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PERFORMANCE IMPROVEMENTS OF SELF-TUNING CONTROLLERS BY MULTISTEP HORIZONS - THE MUSMAR APPROACH

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AUTOMATICA 1984年第5期20卷 681-699页

作者： GRECO, C MENGA, G MOSCA, E ZAPPA, G UNIV FIRENZE DIPARTIMENTO SISTEMI & INFORMAT I-50139 FIRENZE ITALY

The problem of adaptively controlling a linear multivariable plant according to a quadratic cost functional defined over a control horizon of arbitrary length is discussed. In this context, the proposed algorithm, referred to by the acronym MUSMAR, is shown to be a natural generalization of standard self-tuning controllers. By increasing the control horizon length, the MUSMAR closely approximates a steady-state LQG controller inheriting the intrinsic robustness of LQG design. Analysis and simulations give evidence of several attractive features of the MUSMAR self-tuner when applied to plants for which standard adaptive controllers fail to converge or yield an unacceptable performance.

关键词： Adaptive control least-squares estimation linear optimal regulator recursive algorithms self-tuning regulators

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A PERSPECTIVE ON CONVERGENCE OF ADAPTIVE-CONTROL algorithms

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AUTOMATICA 1984年第5期20卷 519-531页

作者： GOODWIN, GC HILL, DJ PALANISWAMI, M Department of Electrical and Computer Engineering University of Newcastle New South Wales 2308 Australia

This paper presents an overview of the current status of convergence theory for adaptive control algorithms. Rather than giving a comprehensive survey, the paper aims to emphasize the conceptual common ground between ... 详细信息

关键词： Adaptive control convergence least-squares estimation model reference adaptive control parameter estimation pole placement recursive algorithms robust control stochastic control

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