Optimal Exact Path-Following for Constrained Differentially Flat Systems
We propose a dynamic optimization approach to calculate optimal feedforward controls for exact path-following problems of differentially flat systems. Besides the derivation of a small dimensional optimal control problem, we provide easily checkable conditions on the existence of inputs guaranteeing that a given path is exactly followable in the presence of constraints on states and inputs. Our approach is based on the projection of the feedforward controlled, nonlinear MIMO dynamics along a geometric path onto a linear single-input system in Brunovsky normal form. The presented results indicate how the computation of admissible trajectories for set-point changes can be simplified by relying on steady state consistent paths. The set-point change of a Van de Vusse reactor is considered as an example.