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Summary. The problem studied here is a shortest path problem of the type encountered in sub-Riemannian geometry. It is distinguished by special structures related to its Lie group setting and the Z2 graded structure on the relevant Lie algebra. In spite of the fact that the first order necessary conditions lead to differential equations that are integrable in terms of elementary functions, in this case there remain questions related to the existence of appropriate values for the parameters which appear. In this paper we treat the problem in some generality but establish the existence of suitable parameter values only in the case of the general linear group of dimension two. [ABSTRACT FROM AUTHOR]

In his Doctoral thesis and subsequent publications (e.g., [1]) Keith Glover explored the parameterization of multivariable time invariant linear systems investigating identifiability and suitable standard forms for use in system identification. Over the years the idea of identifiability has come to play an important role in the literature. In this paper we describe some new results centering around a quantitative measure of identifiability defined in terms of a suitable Gramian. The motivation comes from a desire to provide a quantitative evaluation of the so-called “two dimensional method” widely used in nuclear magnetic resonance (NMR) spectroscopy and we provide this in terms of a Cramer-Rao bound. In the final section we expand the scope of these ideas, providing a more general system theoretic development which discusses a new role for feedback in system identification. [ABSTRACT FROM AUTHOR]

The Hamiltonians that arise in optimal control include some that correspond directly to physical systems and some that do not. For those that do, one can often identify an appropriate quantization procedure and thus associate a Schrodinger equation with an optimal control problem. However, optimal control problems that can not be converted to Lagrangian form, such as those that arise when the system is controllable because of a Lie bracket effect, are more difficult and no straight forward method seems to exist. The purpose of this paper is to describe some possibilities for assigning a Schrodinger equation to such systems. We do not attempt to formulate a general theory but focus on selected examples. We show that this approach leads to interesting "quantum" nonholonomic phenomena. [ABSTRACT FROM AUTHOR]

It is clear that digital signal processing is growing in importance, fulfilling functions that were once carried out exclusively by analog means. At the same time the analog point of view, as represented by neural networks and adaptive control is also developing in new directions. Prompted by these considerations, this paper attempts to put into perspective recent work on analog computing. Some basic definitions are proposed and used to classify some examples from the literature. [ABSTRACT FROM AUTHOR]