Global structural approximate controllability of polynomial nonlinear systems

Abstract

In this paper sufficient conditions for the global structural approximate controllability of polynomial sampled data systems will be derived based on a graph theoretical approach. The results obtained are an extension of the results of [1] from linear systems to polynomial systems. In a first step the notions of polynomial sampled data systems, structural controllability, and bundle graphs of those systems will be introduced. After a definition of general conductance and storage elements of a bundle graph, a theorem will be proved that provides sufficient conditions for the global structural approximate controllability of polynomial systems for large values of the state varaibles in a next step. In a third step a procedure will be presented for deriving a bundle graph cactus hedge from a given bundle graph. In a last step the theorem of step two will be extended to the whole state space using the well known concept of the mapping degree of a function.