Reduced-complexity interpolating control with periodic invariant sets

A construction of interpolating wavelets on invariant sets

We introduce the concept of a refinable set relative to a family of contractive mappings on a metric space, and demonstrate how such sets are useful to recursively construct interpolants which have a multiscale structure. The notion of a refinable set parallels that of a refinable function, which is the basis of wavelet construction. The interpolation points we recursively generate from a refin...

On invariant sets topology

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

Reduced Complexity Control Systems

This paper discusses methods for the analysis and design of systems controlled, at least in part, by finite state controllers, such as might be found in adaptive or highly autonomous robotic systems. We focus on the role that feedback can play in simplifying the characterization of trajectories and, in particular, the extent to which elementary feedback rules based on finite state automata can ...

Fixed Point Indices and Invariant Periodic Sets of Holomorphic Systems

This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will prove Needham’s theorem in a more general version. 1. Fixed point indices of holomorphic mappings Let C be the complex vector space of dimension n, let U be a...

Almost Periodic Invariant Vector Sets in a Metric Vector Space.