Reduced order modeling of nonlinear control systems

Abstract

We consider the problem of model reduction for nonlinear control systems. We introduce the concept of input normal form of degree d and show that a sufficiently smooth nonlinear control system can always be brought to this form by local changes of state coordinates. The changes of coordinates are not uniquely defined but the resulting normal form of the controllability and observability functions are if d ≤ 6. The parameters in this normal form indicates the relative importance of the state coordinates to the input output map of the control system. Then we offer a new interpretation of linear balanced truncation and show how it can be extended to nonlinear system. Finally we offer new estimates of error between the full and reduced Hankel maps. © 2008 Springer-Verlag.