The aim of this dissertation is to examine optimal control of a class of system known as
differentially flat systems. These are systems in which the states and inputs can be
expressed as functions of an output vector and its derivatives. The flat outputs can be
described as components of the mapping from the system space to a smaller dimensional
space. This property allows one to systematically generate feasible trajectories in a relatively
simple way. Using this property, optimal control formulations can be transformed into a …

As we move to increasingly complex cyber–physical systems (CPS), new approaches are
needed to plan efficient state trajectories in real-time. In this paper, we propose an approach
to significantly reduce the complexity of solving optimal control problems for a class of CPS
with nonlinear dynamics. We exploit the property of differential flatness to simplify the Euler–
Lagrange equations that arise during optimization, and this simplification eliminates the
numerical instabilities that plague optimal control in general. We also present an explicit …