Computing Balanced Realizations for Nonlinear Systems

Abstract

In 1993, Scherpen generalized the balanced truncation method to the nonlinear setting. However, the Scherpen procedure is not easily computable and has not yet been applied in practice. We offer methods, tools, and algorithms for computing the energy functions and coordinate transformations involved in the Scherpen theory and procedure for nonlinear balancing. We then apply our approach to derive, for the first time, balanced representations of nonlinear state-space models. 1 Introduction This paper addresses the problem of computability pertaining to the Scherpen theory and procedure for balancing of nonlinear systems [1, 2]. We offer methods, tools, and algorithms toward computing balanced realizations for asymptotically stable affine nonlinear control systems, i.e., state-space models of the form x(t)=f (x(t)) + m X i=1 g i (x(t)) u i (t) (1) y(t)=h (x(t)) (2) where u =(u 1 ,...,u m ) # U # IR m , y =(y 1 ,...,y p ) # IR p ,andx =(x 1 ,...,x n ) are local coordinates for...