Inversion of linear and nonlinear observable systems with series-defined output trajectories

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.