Aerodynamic Envelope Computation for Safe Landing of the HL-20 Personnel Launch Vehicle Using Hybrid Control

The main limitation of existing computational tools for solving hybrid system reachability problems is that, due to the exponential growth of the computation with the dimension of the continuous state space, the tools can be applied effectively to relatively low dimensional problems (typically 1-4 dimensions). In this paper we adopt a two time scale approach to extend the use of hybrid system reachability tools to six dimensions, thus making them applicable to a number of interesting case studies in the area of aeronautics. To prove the effectiveness of our approach, we apply it in the aerodynamic envelope computation for safe landing of the HL-20 personnel launch vehicle (PLV). The mathematical model of the PLV that is used is a three degree of freedom (six state) nonlinear point mass model having three discrete aerodynamic modes (supersonic, transonic, subsonic) and several state constraints for the final approach phase. The results show that it is feasible to do exacting computations for hybrid systems with nonlinear continuous dynamics in higher dimensions, if one can exploit additional structure in the model (in our case, the separation into slow and fast dynamics)