Tracking controller design for nonlinear dynamics using differential parameterizations

Many technical processes can be described by a set of differential equations, which is called a dynamics. In this context, trajectory tracking means that the dynamics are influenced such that its states evolve on a predefined reference trajectory. A special class of dynamics is the class of differentially flat dynamics, which are characterized, roughly speaking, by the fact that all states and inputs of a dynamics can be differentially parameterized with an (eventually fictitious) “flat” output. Using the differential parameterization, the design of feedforward and feedback tracking controllers with respect to the flat output is very intuitive. In this dissertation it is shown that differential parameterizations can also be a useful tool for the tracking controller design with respect to non-flat outputs and even for non-flat dynamics. Differential flatness has originally been introduced in a differential algebraic framework, but also a differential geometric framework for flatness has been established using the concept of infinite prolongations of vector fields and Lie-Bäcklund equivalence. As the differential geometric setting allows a direct comparison with other differential geometric concepts for feedback linearization and trajectory tracking, all results on differential parameterizations of nonlinear dynamics in this thesis have been derived using the differential geometric approach.