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Optimal control for a new class of singularly perturbed linear systems

AUTOMATICA 2017年 81卷 203-208页

作者： Kodra, Kliti Gajic, Zoran Rutgers State Univ Dept Elect & Comp Engn 94 Brett Rd Piscataway NJ 08854 USA

Singularly perturbed linear control systems have been traditionally studied with one-vector input that controls both the slow and fast state variables. Motivated by examples of real physical systems, in this paper we extend the study to corresponding two-vector input systems. We have identified several classes of real physical singularly perturbed systems that can be more efficiently controlled using two-vector inputs. In such systems, one vector input is used to control the slow state space variables and the other vector input is used to control the fast state variables. This control structure offers more flexibility controlling given systems and appears to be more effective, We study the linear-quadratic regulator (LQR) problem for this new class of singularly perturbed systems and develop a numerical algorithm based on fixed-point iterations to obtain its solution. The latter is obtained in terms of reduced-order sub-problems which avoid possible numerical stiffness issues and are computationally advantageous for large scale systems. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Linear-quadratic regulators Optimal control recursive algorithms Singular perturbations

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Non-linear minimum variance state-space-based estimation for discrete-time multi-channel systems

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IET SIGNAL PROCESSING 2011年第4期5卷 365-378页

作者： Grimble, M. J. Univ Strathclyde Ind Control Ctr Glasgow G1 1QE Lanark Scotland

A new state equation and non-linear operator-based approach to estimation is introduced for discrete-time multi-channel systems. This is a type of deconvolution or inferential estimation problem, where a signal enters a communications channel involving both non-linearities and transport delays. The measurements are corrupted by a coloured noise signal, which is correlated with the signal to be estimated both at the inputs and outputs of the channel. The communications channel may include either static or dynamic non-linearities represented in a general non-linear operator form. The optimal non-linear estimator is derived in terms of the state equations and non-linear operators that describe the system. The algorithm is relatively simple to derive and to implement in the form of a recursive algorithm. The main advantage of the approach is the simplicity of the non-linear estimator theory and the straightforward structure of the resulting solution. The results may be applied to the solution of channel equalisation problems in communications or fault detection problems in control applications.

关键词： equations of state deconvolution recursive algorithms Communication Research signals Colored noise noise signal

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A recursive Newton type algorithm for digital frequency relaying

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ELECTRIC POWER SYSTEMS RESEARCH 1996年第1期36卷 67-72页

作者： Terzija, VV Djuric, MB Jeremic, NZ Faculty of Electrical Engineering University of Belgrade Bulevar Revolucije 73 PO Box 816 11001 Belgrade Yugoslavia

This paper presents a new recursive Newton type algorithm devoted to frequency relaying. The algorithm is designed from the nonrecursive Newton type algorithm and recursive least error squares algorithm. The frequency is estimated from the uniformly sampled voltage signal. The algorithm testing based on computer simulated and experimentally obtained data record processing confirmed the good features of the algorithm developed. Due to its computational efficiency, the algorithm is suitable for various real-time power system measurement applications.

关键词： frequency relaying data processing recursive algorithms

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CHEBYSHEV POLYNOMIAL APPROXIMATION FOR ACTIVATION SIGMOID FUNCTION

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NEURAL NETWORK WORLD 2012年第4期22卷 387-393页

作者： Vlcek, Miroslav Czech Tech Univ Fac Transportat Sci Dept Appl Math CR-16635 Prague Czech Republic

An alternative polynomial approximation for the activation sigmoid function is developed here. It can considerably simplify the input/output operations of a neural network. The recursive algorithm is found for Chebysh... 详细信息

关键词： Sigmoid function Chebyshev polynomials recursive algorithms

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A recursive LU DECOMPOSITION ALGORITHM

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 1994年第2期7卷 48-52页

作者： TWIG, Y KASTNER, R Department of Electrical Engineering Physical Electronics Tel Aviv University Tel Aviv 69978 Israel

A recursive LU decomposition scheme extends the capabilities of nonrecursive algorithms for the reduction of computation time when geometrical modifications are made to a precomputed scatterer. Significant savings are achieved for cases of many different attachments, or when the initial scatterer is amenable to a particular efficient solution. (C) 1994 John Wiley & Sons, Inc.

关键词： recursive algorithms LU DECOMPOSITION INTEGRAL EQUATIONS MOMENT METHOD

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Algorithm 865: Fortran 95 subroutines for cholesky factorization in block hybrid format

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 2007年第1期33卷 8.1-8.5页

作者： Gustavson, Fred G. Reid, John K. Wasniewski, Jerzy IBM Corp Thomas J Watson Res Ctr Yorktown Hts NY 10598 USA Rutherford Appleton Lab Atlas Ctr Didcot OX11 0QX Oxon England Tech Univ Denmark DK-2800 Lyngby Denmark

We present subroutines for the Cholesky factorization of a positive-definite symmetric matrix and for solving corresponding sets of linear equations. They exploit cache memory by using the block hybrid format proposed by the authors in a companion article. The matrix is packed into n(n + 1)/2 real variables, and the speed is usually better than that of the LAPACK algorithm that uses full storage (n(2) variables). Included are subroutines for rearranging a matrix whose upper or lower-triangular part is packed by columns to this format and for the inverse rearrangement. Also included is a kernel subroutine that is used for the Cholesky factorization of the diagonal blocks since it is suitable for any positive-definite symmetric matrix that is small enough to be held in cache. We provide a comprehensive test program and simple example programs.

关键词： algorithms performance real symmetric matrices positive definite matrices Cholesky factorization and solution recursive algorithms novel packed matrix data structures linear systems of equations BLAS

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OPTIMAL ESTIMATION FOR THE SATELLITE ATTITUDE USING STAR TRACKER MEASUREMENTS

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AUTOMATICA 1986年第4期22卷 477-482页

作者： LO, JTH Department of Mathematics University of Maryland Baltimore County Catonsville MD 21228 U.S.A.

An optimal estimation scheme is presented, which determines the satellite attitude using the gyro readings and the star tracker measurements of a commonly used satellite attitude measuring unit. The scheme is mainly based on the exponential Fourier densities that have the desirable closure property under conditioning. By updating a finite and fixed number of parameters, the conditional probability density, which is an exponential Fourier density, is recursively determined. Simulation results indicate that the scheme is more accurate and robust than extended Kalman filtering. It is believed that this approach is applicable to many other attitude measuring units. As no linearization and approximation are necessary in the approach, it is ideal for systems involving high levels of randomness and/or low levels of observability and systems for which accuracy is of overriding importance.

关键词： estimation exponential Fourier densities gyroscopes Optimal filtering recursive algorithms spacecraft attitude

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SIMULTANEOUS PARAMETER TRACKING AND STATE ESTIMATION IN A LINEAR-SYSTEM

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AUTOMATICA 1993年第4期29卷 1041-1052页

作者： HAVLENA, V KYOTO UNIV DEPT ELECT ENGN 2 KYOTO 606 JAPAN

The task of simultaneous tracking of time-varying parameters and estimation of the state is treated for a linear system described by a time-varying input-output ARMAX or Delta model with known c (noise) parameters. First, a Bayesian approach-based conceptual solution is presented. Then it is shown that utilizing the properties of the observer canonical state model, algebraic recursion operating on the joint parameter and state mean and covariance matrix can be obtained with no approximation involved. Several illustrative examples are included.

关键词： ADAPTIVE SYSTEMS KALMAN FILTERS PARAMETER ESTIMATION STATE ESTIMATION recursive algorithms COMPUTATIONAL METHODS

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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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MEASUREMENT PROBLEMS ARISING FROM THE USE OF A recursive ALGORITHM FOR MODEL IDENTIFICATION OF ELECTRICAL SYSTEMS

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 1992年第2期41卷 240-245页

作者： BERNIERI, A BETTA, G DAPUZZO, M UNIV SALERNO INST ELECTR ENGN I-84081 BARONISSI ITALY NAPLES UNIV DEPT COMP SCI I-80125 NAPLES ITALY

The use of parameter estimation techniques in practical applications requires accurate analysis of the associated measurement and computation problems. With reference to an already proposed model identification procedure, this paper deals with the experimental tests carried out in order to highlight problems and to find the most appropriate solutions. In particular, a synchronization method is described, and some suggestions concerning the optimal working conditions of all the necessary devices are reported.

关键词： recursive algorithms model identification Working Conditions Electrical systems

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