Difference approximations for higher index differential-algebraic systems with applications in trajectory control

The equations which describe a trajectory prescribed path control (TPPC) problem naturally form a system of nonlinear semi-explicit, differential-algebraic equations (DAES) with index greater than one. It is known that not all implicit systems may be solved stably by the k-step backward difference formulas (BDF), yet these methods do produce convergent numerical solutions to some semi-explicit systems. Convergence theory of the BDF for DAE systems are briefly reviewed, before discussing our numerical experience with the simplest BDF when applied to an index three, TPPC problem that arose in the reentry control of the Space Shuttle.