On the Computation of Differentially Flat Inputs

Differential flatness and methods based on this property have proved to be very fruitful for tracking controllers and trajectory planning of nonlinear systems. As a dual to the concept of differentially flat outputs, this contribution deals with the computation of flat inputs, and thus with the problem of actuator placement. Given a mathematical description of a system’s behavior and a desired output, we propose an algorithm that constructs such inputs for observable systems. We show that there are no integrability problems which are typical for flat output computations, and exemplify this by an example. For non-observable systems, we show that an additional constraint needs to be fulfilled. It is not obvious how to incorporate this into an algorithm.