Differential algebra techniques for space applications

This project investigates the utility of differential algebra (DA) techniques applied to the problem of orbital dynamics with initial uncertainties in the orbital determination of the involved bodies. The use of DA theory allows the splitting of a common Monte Carlo simulation in two parts: the generation of a Taylor map of the final states with regard to the perturbation in the initial coordinates, and the evaluation of the map for many points. A propagator is implemented exploiting DA techniques, and tested in the field of asteroid impact risk monitoring with the potentially hazardous 2011 AG5 and 2007 VK184 as test cases. Results show that the new method is able to simulate 2.5 million trajectories with a precision good enough for the impact probability to be accurately reproduced, while running much faster than a traditional Monte Carlo approach (in 1 and 2 days, respectively).

Uniform Distributed Pushdown Automata Systems.

We consider here uniform distributed pushdown automata systems (UDPAS), namely distributed pushdown automata systems having all components identical pushdown automata. We consider here just a single protocol for activating/deactivating components, namely a component stays active as long as it can perform moves, as well as two ways of accepting the input word: by empty stacks (all components have empty stacks) or by final states (all components are in final states), when the input word is completely read. We mainly investigate the computational power of UDPAS accepting by empty stacks and a few decidability and closure properties of the families of languages they define. Some directions for further work and open problems are also discussed.