A survey of model reference adaptive techniques-Theory and applications

Computing derivatives of eigenvalues and eigenvectors is of considerable importance in mathematics, physics, and engineering. These derivatives are essential for sensitivity analysis, which is used to study the effect of change in various parameters of an eigensystem on its performance. General solutions of eigenfunction s' derivatives have not been available. In this paper, exact analytical solutions for the wth derivatives of unrepeated eigenvalues and corresponding eigenvectors are given for general nonlinear and linear eigenvalue problems. The application of the theory is illustrated with examples.

Exact nth Derivatives of Eigenvalues and Eigenvectors

This survey paper presents a comprehensive review of work in the field of non-linear oscillations. A brief discussion of second-order systems is followed by a presentation of exact criteria, approximate analytical methods and computational techniques for limit cycles in single variable systems. Multivariate systems are then covered from an analogous viewpoint which allows the reader to clearly identify both how single variable methods have been extended and the possibilities for further research. Particular emphasis is placed on describing function methods since it is believed that, where exact solutions are not possible, the approach may not only give approximate solutions but provides good insight for further computational or simulation studies. The coverage is essentially restricted to continuous lumped parameter systems and includes both free and forced oscillations. Several applications of the theories in various fields of engineering and science are discussed and indicate the broad interest in non-l...

A survey on non-linear oscillations

The method presented here is an extension of the multiple shooting algorithm in order to handle multipoint boundary-value problems and problems of optimal control in the special situation of singular controls or constraints on the state variables. This generalization allows a direct treatment of (nonlinear) conditions at switching points. As an example a model of optimal heating and cooling by solar energy is considered. The model is given in the form of an optimal control problem with three control functions appearing linearly and a first order constraint on the state variables. Numerical solutions of this problem by multiple shooting techniques are presented.

Numerical computation of singular control problems with application to optimal heating and cooling by solar energy

This paper addresses the problem of controlling the dynamic (or oscillatory) stability of Power Systems, in the following setting: 1) Use of detailed, high dimension linear invariant models, in a multimachine environment.

Arthur L. Greensite

Papers

Elements of Modern Control Theory