Absolute Equivalence of Pfaffian Modules and Applications to Nonlinear Control Theory

Willem Sluis, Fields Institute

In 1914, Elie Cartan defined the notion of absolute equivalence for Pfaffian systems of rank n defined on an open subset of R^n. He was motivated by the problem to determine which systems of ordinary differential equations, underdetermined by one, admit a general solution that may be found using only differentiation and algebra. Using the notion of absolute equivalence Cartan solved this problem. In this talk, I will indicate what absolute equivalence is, and indicate its relevance for nonlinear control theory, in particular the problem of dynamic feedback linearization. Furthermore, I will present some new examples where absolute equivalence will be used to find nonlinear normal forms.