Approximately linear tracking control of nonlinear systems

An elegant approach to control nonlinear state-space systems is the exact input-to-state linearization, where a nonlinear change of coordinates combined with a nonlinear feedback law yields a linear controllable system. In this contribution, we treat the single-input case, where input-to-state linearizability is equivalent to flatness. Sufficient and necessary existence conditions are well-known, but quite restrictive. We propose the design of a tracking controller for flat single-input systems, where the explicit knowledge of the flat output is not required. Our approach is based on a series expansion of the tracking error along a given reference trajectory. The controller gain can even be computed for non-flat systems with regular controllability matrix. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)