Computing feasible trajectories for control-constrained systems: the PVTOL example

In this paper we provide a new strategy to explore feasible trajectories of nonlinear systems, that is to find curves that satisfy the dynamics as well as point- wise state-input constraints. This strategy is interesting itself in understanding the behavior of the system especially in critical conditions, and represents a useful tool that can be used to perform trajectory tracking in presence of constraints. The strategy is based on a novel optimization technique, introduced by Hauser, to find regularized solutions for point-wise constrained optimization of trajectory functionals. The strategy is applied to the PVTOL, a simplified model of a real aircraft that captures the main features and challenges of the real model.