Fuel-Optimal Spacecraft Rendezvous with Hybrid On–Off Continuous and Impulsive Thrust

J = cost function N = number of impulses NLT = number of low-thrust-independent thrusters p = primer-vector magnitude p = primer vector pm = primer-vector absolute maximum r = relative position vector rj = space collocation of the jth impulse tf = final time tint = intermediate time tj = time instant of the jth impulse application tm = midcourse time corresponding to the primer absolute maximum t0 = initial time u = thrust unit vector V = relative velocity vector x, y, z = coordinates in the local vertical, local horizontal coordinate system Vj = jth impulse vector t tj = Dirac’s delta at time tj # = anomaly on the circular orbit r = position adjoint vector V = velocity adjoint vector = control vector magnitude t = state transition matrix for the Clohessy–Wiltshire equations t = convolution integral matrix for the Clohessy– Wiltshire equations due to optimal unbounded control !LVLH = angular velocity of the local vertical, local horizontal coordinate system