  This paper presents a new fast and robust algorithm that provides
fuel-optimal impulsive control input sequences that drive a linear time-variant
system to a desired state at a specified time. This algorithm is applicable to
a broad class of problems where the cost is expressed as a time-varying
norm-like function of the control input, enabling inclusion of complex
operational constraints in the control planning problem. First, it is shown
that the reachable sets for this problem have identical properties to those in
prior works using constant cost functions, enabling use of existing algorithms
in conjunction with newly derived contact and support functions. By
reformulating the optimal control problem as a semi-infinite convex program, it
is also demonstrated that the time-invariant component of the commonly studied
primer vector is an outward normal vector to the reachable set at the target
state. Using this formulation, a fast and robust algorithm that provides
globally optimal impulsive control input sequences is proposed. The algorithm
iteratively refines estimates of an outward normal vector to the reachable set
at the target state and a minimal set of control input times until the
optimality criteria are satisfied to within a user-specified tolerance. Next,
optimal control inputs are computed by solving a quadratic program. The
algorithm is validated through simulations of challenging example problems
based on the recently proposed Miniaturized Distributed Occulter/Telescope
small satellite mission, which demonstrate that the proposed algorithm
converges several times faster than comparable algorithms in literature.
