Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Steering nonholonomic systems in chained form

The authors introduce a nilpotent form, called a chained form, for nonholonomic control systems. For the case of a nonholonomic system with two inputs, they give constructive conditions for the existence of a feedback transformation which puts the system into chained form, and show how to steer the system between arbitrary states. Examples are presented for steering a car and a car with a trailer attached: other examples can be found in the areas of space robotics and multifingered robot hands. The present results also have applications in the area of nilpotentization of distributions of vector fields on R^n

Accessibility and singular foliations

In Part One we study the partition of a finite-dimensional manifold M into the accessible sets of an arbitrary system A of isotopy families of local diffeomorphisms of M and, in particular, into the accessible sets of an arbitrary system of differentiable vectorfields on M. In Part Two we generalize the methods of Part One to study the integrability of singular distributions on infinite-dimensional manifolds. In Part Three we return to finite-dimensional manifolds and use the results of Part One to study in detail the contrasting properties of integrability and irreducibility of systems of vectorfields on M

Nonsmooth controllability theory and an example

Extends results in local controllability analysis for multiple model driftless affine (MMDA) control systems. Such controllability results can be interpreted as non-smooth extensions of Chow's theorem, and use a set-valued Lie bracket. In particular, we formulate controllability in terms of generalized differential quotients. Additionally, we present an extensive example in order to illustrate how these results can provide insight into the control of some specific physical systems. Moreover, the paper indicates that a multiple model system consisting of individually controllable models is not necessarily controllable

Feedback stabilization of bilinear control systems

In this dissertation we study the region in which a bilinear control system is feedback stabilizable. In particular, we prove the equivalence of exponential stability and asymptotic stability using measurable feedback laws. Also we find a necessary and sufficient condition for feedback stabilization in terms of the Lyapunov spectrum. The maximal stabilizable region is discussed and some open questions are presented

The Irreducibility of the Space of Curves of Given Genus

Mathematic