An Iterative Solution to Stable Inversion of Nonminimum Phase Systems

This paper addresses the inversion of a nonlinear system of the form ¿ = f(x) + g(x)u, y = h(x) from the perspective of nonlinear geometric control theory. We use the notion of zero dynamics for obtaining stable, though noncausal, inverses for nonminimum phase systems. This contrasts with the causal inverses proposed by Hirschorn where unstable zero dynamics result in unbounded solutions to the inverse problem. Our results reduce to those of Hirschorn in the case of stable zero dynamics, however. The main results include: equivalence of stable inversion to two point boundary value problems; local existence and uniqueness of solution; an iterative numerical procedure; and an example showing superior performance of inversion over nonlinear regulation for output tracking.