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sequential gradient-restoration algorithm for optimal control problems

Journal of Optimization Theory and Applications 1970年第4期5卷 235-282页

作者： Miele, A. Pritchard, R.E. Damoulakis, J.N. Department of Mechanical and Aerospace Engineering and Materials Science Rice University Houston Texas United States

This paper considers the problem of minimizing a functional I which depends on the state x(t), the control u(t), and the parameter π. Here, I is a scalar, x an n-vector, u an m-vector, and π a p-vector. At the initial point, the state is prescribed. At the final point, the state x and the parameter π are required to satisfy q scalar relations. Along the interval of integration, the state, the control, and the parameter are required to satisfy n scalar differential equations. A sequential algorithm composed of the alternate succession of gradient phases and restoration phases is presented. This sequential algorithm is contructed in such a way that the differential equations and boundary conditions are satisfied at the end of each iteration, that is, at the end of a complete gradient-restoration phase;hence, the value of the functional at the end of one iteration is comparable with the value of the functional at the end of any other iteration. In the gradient phase, nominal functions x(t), u(t), π satisfying all the differential equations and boundary conditions are assumed. Variations Δx(t), Δu(t), Δπ leading to varied functions {Mathematical expression}(t), ũ(t), {Mathematical expression} are determined so that the value of the functional is decreased. These variations are obtained by minimizing the first-order change of the functional subject to the linearized differential equations, the linearized boundary conditions, and a quadratic constraint on the variations of the control and the parameter. Since the constraints are satisfied only to first order during the gradient phase, the functions {Mathematical expression}(t), ũ(t), {Mathematical expression} may violate the differential equations and/or the boundary conditions. This being the case, a restoration phase is needed prior to starting the next gradient phase. In this restoration phase, the functions {Mathematical expression}(t), ũ(t), {Mathematical expression} are assumed to be the nominal functions. Variation

关键词： Optimal Control Problem Varied Function sequential algorithm Nominal Function Quadratic Constraint

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sequential Abstract-State Machines Capture sequential algorithms

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ACM Transactions on Computational Logic 2000年第1期1卷 77-111页

作者： Gurevich, Yuri Microsoft Research One Microsoft Way Redmond WA 98052 United States

We examine sequential algorithms and formulate a sequential-time postulate, an abstractstatepostulate, and a bounded-exploration postulate. Analysis of the postulates leads us tothe notion of sequential abstract-state machine and to the theorem in the title. First we treatsequential algorithms that are deterministic and noninteractive. Then we consider sequentialalgorithms that may be nondeterministic and that may interact with their environments. © 2000, ACM. All rights reserved.

关键词： Abstract-state machine algorithms Design Documentation Executable specification Languages sequential algorithm sequential ASM thesis Specification Theory Turing's thesis

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Efficient Controls for Finitely Convergent sequential algorithms

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 2010年第2期37卷 14-14页

作者： Chen, Wei Herman, Gabor T. CUNY Grad Ctr Dept Comp Sci New York NY 10016 USA

Finding a feasible point that satisfies a set of constraints is a common task in scientific computing;examples are the linear feasibility problem and the convex feasibility problem. Finitely convergent sequential algorithms can be used for solving such problems;an example of such an algorithm is ART3, which is defined in such a way that its control is cyclic in the sense that during its execution it repeatedly cycles through the given constraints. Previously we found a variant of ART3 whose control is no longer cyclic, but which is still finitely convergent and in practice usually converges faster than ART3. In this article we propose a general methodology for automatic transformation of finitely convergent sequential algorithms in such a way that (1) finite convergence is retained, and (2) the speed of convergence is improved. The first of these properties is proven by mathematical theorems, the second is illustrated by applying the algorithms to a practical problem.

关键词： algorithms Design Experimentation Performance Theory Algebraic reconstruction technique cyclic subgradient projections finite convergence feasibility problem sequential algorithm

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Enhancement of log Mel power spectra of speech using a phase-sensitive model of the-acoustic environment and sequential estimation of the corrupting noise

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IEEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING 2004年第2期12卷 133-143页

作者： Deng, L Droppo, J Acero, A Microsoft Res Redmond WA 98052 USA

This paper presents a novel speech feature enhancement technique based on a probabilistic, nonlinear acoustic environment model that effectively incorporates the phase relationship (hence phase sensitive) between the clean speech and. the corrupting noise in the acoustic distortion process. The core of the enhancement algorithm is the MMSE (minimum mean square error) estimator for the log Mel power spectra of clean speech based on the phase-sensitive environment model, using highly efficient single-point, second-order Taylor series expansion to approximate the joint probability of clean and noisy speech modeled as a multivariate Gaussian. Since a noise estimate is required by the MMSE estimator, a high-quality, sequential noise estimation algorithm is also developed and presented. Both the noise estimation and speech feature enhancement algorithms are evaluated on the Aurora2 task of connected digit recognition. Noise-robust speech recognition results demonstrate that the new acoustic environment model which takes into account, the relative phase in speech and noise mixing is superior to the earlier environment model which discards the phase under otherwise identical experimental conditions. The results also show that the sequential MAP (maximum a posteriori) learning for noise estimation is better. than the sequential ML (maximum likelihood) learning, both evaluated under the identical phase-sensitive MMSE enhancement condition.

关键词： noise estimate noise-robust ASR phase-sensitive acoustic environment model sequential algorithm speech feature enhancement

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COMPUTATIONAL-COMPLEXITY OF sequential SEQUENCE ESTIMATION FOR INTERSYMBOL INTERFERENCE CHANNELS

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IEEE TRANSACTIONS ON COMMUNICATIONS 1993年第2期41卷 332-337页

作者： XIONG, FQ DAI, QY SHWEDYK, E UNIV MANITOBA DEPT ELECT ENGNWINNIPEG R3T 2N2MANITOBACANADA UNIV MANITOBA DEPT ELECT & COMP ENGNWINNIPEG R3T 2N2MANITOBACANADA

A receiver consisting of a whitened matched filter (WMF) followed by a sequential algorithm (SA) had been developed previously for intersymbol interference (ISI) channels. The channel-WMF system can be modeled as a finite-state machine (FSM). This paper presents an analysis of SA computational complexity. To determine the computational complexity, the FSM can be interpreted as a special convolutional encoder followed by a binary symbol to Q-ary symbol mapping. It follows that the computational distribution is Pareto, and that there exists a computational cutoff rate R(comp). For the uncoded data considered, the rate is fixed and the R(comp) criterion translates into a signal-to-noise ratio (SNR) criterion, i.e., for bounded computation per node, the SNR should exceed SNR(comp). An upper bound SNR(comp)' on SNR(comp) is found analytically by assuming a uniform input distribution. Arimoto's iteration equations are adapted to find the true SNR(comp) numerically.

关键词： filtration system complexity classes sequential algorithm convolutional coder matched filters finite state machines state machines Map symbols intersymbolic interference

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sequential SEQUENCE ESTIMATION FOR MULTIPLE-CHANNEL SYSTEMS WITH INTERSYMBOL AND INTERCHANNEL INTERFERENCE

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IEEE TRANSACTIONS ON COMMUNICATIONS 1993年第2期41卷 322-331页

作者： XIONG, FQ SHWEDYK, E UNIV MANITOBA DEPT ELECT ENGN WINNIPEG R3T 2N2 MANITOBA CANADA UNIV MANITOBA DEPT ELECT & COMP ENGN WINNIPEG R3T 2N2 MANITOBA CANADA

A vector sequential sequence estimator is proposed for multiple-channel transmission systems with both intersymbol interference (ISI) and interchannel interference (ICI). Both finite ISI-ICI and infinite ISI-ICI are considered. The estimator consists of a multiple-dimensional whitened matched filter and a vector sequential decoder. The metric of the sequential algorithm is derived and the algorithm's performance analysis is given. Computer simulation results for a two-dimensional finite ISI-ICI channel and a two-dimensional infinite ISI-ICI channel are presented. Analysis and simulation show that the symbol error probability of the vector sequential algorithm is essentially the same as maximum likelihood sequence estimation via the vector Viterbi algorithm (VA), while its average computational complexity is much less, although computation per symbol is a random variable with the Pareto distribution. There exists a signal-to-noise ratio SNR(comp) above which the ensemble average computation is bounded. An upper bound on the SNR(comp) is found.

关键词： complexity classes Random variable sequential algorithm sequential intersymbol MULTICHANNEL Error probability Interchannel interference maximum likelihood sequence estimation Pareto distribution

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Iterative improvement of parameter estimation for model migration by means of sequential experiments

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COMPUTERS & CHEMICAL ENGINEERING 2015年 73卷 128-140页

作者： Luo, Linkai Yao, Yuan Gao, Furong Hong Kong Univ Sci & Technol Dept Chem & Biomol Engn Kowloon Hong Kong Peoples R China Natl Tsing Hua Univ Dept Chem Engn Hsinchu 30013 Taiwan

Determining an optimal design for estimation of parameters of a class of complex models expected to be built at a minimum cost is a growing trend in science and engineering. We adopt a scale-bias adjustment migration strategy for integrating base and new models based on similar nature underlying processes. Further, we propose a Bayesian sequential algorithm for obtaining the statistically most informative data about the migrated model for use in parameter estimation. The benefits of the proposed strategy over traditional approaches presented in recent reported work are demonstrated using Monte Carlo simulations. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Model migration Bayesian Model-based design sequential algorithm

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sequential Multiscale Noise Tuning Stochastic Resonance for Train Bearing Fault Diagnosis in an Embedded System

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2014年第1期63卷 106-116页

作者： Lu, Siliang He, Qingbo Hu, Fei Kong, Fanrang Univ Sci & Technol China Dept Precis Machinery & Precis Instrumentat Hefei 230026 Peoples R China

Multiscale noise tuning stochastic resonance (MSTSR) has been proved to be an effective method for enhanced fault diagnosis by taking advantage of noise to detect the incipient faults of the bearings and gearbox. This paper addresses a sequential algorithm for the MSTSR method to detect the train bearing faults in an embedded system through the acoustic signal analysis. Specifically, the energy operator, digital filter array, and fourth rank Runge-Kutta equation methods are designed to realize the signal demodulation, multiscale noise tuning, and bistable stochastic resonance in sequence. The merit of the sequential algorithm is that it reduces the memory consumption and decreases the computation complexity, so that it can be efficiently implemented in the embedded system based on a low-cost, low-power hardware platform. After the sequential algorithm, the real-valued fast Fourier transform is used to calculate the power spectrum of the analyzed signal. The proposed method has been verified in algorithm performance and hardware implementation by three kinds of practical acoustic signals from defective train bearings. An enhanced performance of the proposed fault diagnosis method is confirmed as compared with several traditional methods, and the hardware performance is also validated.

关键词： Embedded system fault diagnosis multiscale noise tuning sequential algorithm stochastic resonance (SR) train bearing

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sequential extraction of minor components

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NEURAL PROCESSING LETTERS 2001年第3期13卷 195-201页

作者： Chen, TP Amari, SI Murata, N Fudan Univ Dept Math Shanghai 200433 Peoples R China RIKEN Brain Sci Inst Wako Saitama 3510198 Japan

Principal component analysis (PCA) and Minor component analysis (MCA) are similar but have different dynamical performances. Unexpectedly, a sequential extraction algorithm for MCA proposed by Luo and Unbehauen [11] does not work for MCA, while it works for PCA. We propose a different sequential-addition algorithm which works for MCA. We also show a conversion mechanism by which any PCA algorithms are converted to dynamically equivalent MCA algorithms and vice versa.

关键词： minor component sequential algorithm

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Fast parallel and sequential computations and spectral properties concerning band Toeplitz matrices

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Calcolo 1983年第2期20卷 177-189页

作者： Bini, D. Capovani, M. Dipartimento di Matematica dell'Università di Pisa Pisa 56100 Via Buonarroti 2 Italy Dipartimento di Informatica dell'Università di Pisa Pisa 56100 Corso Italia 40 Italy

We exhibit fast computational methods for the evaluation of the determinant and the characteristic polynomial of a (2k+1)-diagonal Toeplitz matrix with elements in the complex field, either for sequential or for parallel computations. A fast algorithm, to achieve one step of Newton's method, is shown to be suitable to compute the eigenvalues of such a matrix. Bounds to the eigenvalues and necessary and sufficient conditions for positive definiteness, which are easy to check, are given either for matrices with scalar elements or for matrices with blocks. In the case in which the blocks are themselves band Toeplitz matrices such conditions assume a very simple form. © 1984 Instituto di Elaborazione della Informazione del CNR.

关键词： Spectral Property Characteristic Polynomial Hermitian Matrix sequential algorithm Positive Definiteness

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