Introduction to linear and nonlinear programming

Singular perturbations and time-scale methods in control theory: Survey 1976-1983

The EM algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models. It is easy to apply in many problems and is stable but slow. The algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the Louis method is performed. Newton-type or other gradient methods are faster and provide error estimates but tend to be unstable and require the analytical evaluation of likelihoods to derive expressions for the score function and (at least) approximations to the Fisher information matrix. The purpose of this paper is to expand on a result by Fisher that permits a unification of EM methodology and Newton methods. The evaluation of the individual observation-by-observation score functions of the incomplete data is a byproduct of the application of the E step of the EM algorithm. Once these become available, the Fisher information matrix may be consistently estimated, and the M step may be replaced by a fast Newton-type step.

A fast improvement to the EM algorithm on its own terms

Publisher Summary This chapter reviews the control of distributed parameter systems. Recent developments in control theory have concentrated primarily on systems whose dynamic behavior can be adequately described by ordinary differential equations. One of the basic prerequisites for the analytical design of control systems is the establishment of an adequate mathematical model of the system to be controlled. The derivation of such a model generally requires considerable physical insight. The model should have the simplest possible form while preserving the dominant system dynamic characteristics. The output of a distributed parameter system may be in the form of a set of spatially-dependent time functions and/or a set of spatially-independent time functions. From the physical standpoint, it is convenient to classify the distributed parameter systems according to their spatial domain properties: (1) fixed-domain systems and (2) variable domain systems. For fixed-domain systems, the system state at any time can be generally specified by a set of functions defined on the spatial domain. For variable domain systems, additional variables specifying the instantaneous boundary position, velocity, etc. are usually necessary to specify the system state completely.

Control of Distributed Parameter Systems1

This paper studies sampled-data control of nonlinear systems using high-gain observers. The observer is designed in continuous time, then discretized using three different discretization methods. Closed-loop analysis shows that the sampled-data controller recovers the performance of the continuous time controller as the sampling frequency and observer gain become sufficiently large. The theory is illustrated by experimental results.

Output feedback sampled-data control of nonlinear systems using high-gain observers

Acceleration by aggregation of successive approximation methods

Multitime Methods for Systems of Difference Equations

Methods of aggregation

Parallel algorithms are developed in the setting of iterative multilevel methods. The constituent parts of the algorithms are dependent rather than independent as in conventional parallel algorithms. We develop cases and conditions wherein this dependence generates a constructive interference in the computation. The resulting parallel algorithms can then be more efficient than serial counterparts.

Constructive interference in parallel algorithms

Convergence of the power method for the algebraic eigenvalue problem is accelerated by an aggregation/disaggregation process. A lower dimensional aggregated eigenvalue problem is created from time to time during the course of the power iteration and the solution of this problem is used to produce acceleration. Analysis and numerical experiments show the effectiveness of the method, the more so, the more poorly conditioned is the original eigenvalue problem.

Aggregation/Disaggregation for Eigenvalue Problems

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