Inversion of Linear and Nonlinear Observable Systems with Series-defined Output Trajectories

TL;DR

This paper develops explicit inverse models for linear and nonlinear observable systems with series-defined outputs, enabling direct inversion using algebraic equations and series methods, requiring only observability.

Contribution

It introduces a novel approach to invertible system modeling using series-defined outputs, applicable to both linear and nonlinear systems, without output redefinition.

Findings

Exact inverse model for linear systems derived.

Approximate inverse model for nonlinear systems on finite intervals.

Inversion relies solely on observability, no output redefinition needed.

Abstract

The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which is a linear combination of some basis functions with arbitrarily free coefficients. The observer canonical form is exploited, and the input-output representation is solved using a series method. It is shown that the only required system characteristic is observability, which implies that there is no need for output redefinition. An exact inverse model is found for linear systems. For general nonlinear systems, a good approximation of the inverse model valid on a finite time interval is found.