On the construction of an optimal feedback control law for time-optimal control problem for a two-input three-dimensional nilpotent system

We derive a set of twenty-four basic formulas for computing feedback control steering any given initial state to the origin and use them to construct an optimal feedback control law for the time-optimal control problem for a two-input three-dimensional nilpotent system. The construction of such an optimal feedback control law is carried out without prior knowledge of the partition of the state space into regions of origination for twenty-four different trajectory types specified in a sufficient family for optimality