  Satellite attitude cotrol is a crucial part of aerospace technology, and
model predictive control(MPC) is one of the most promising controllers in this
area, which will be less effective if real-time online optimization can not be
achieved. Explicit MPC converts the online calculation into a table lookup
process, however the solution is difficult to obtain if the system dimension is
high or the constraints are complex. The lattice piecewise affine(PWA) function
was used to represent the control law of explicit MPC, although the online
calculation complexity is reduced, the offline calculation is still prohibitive
for complex problems. In this paper, we use the sample points in the feasible
region with their corresponding affine functions to construct the lattice PWA
approximation of the optimal MPC controller designed for satellite attitude
control. The asymptotic stability of satellite attitude control system under
lattice PWA approximation has been proven, and simulations are executed to
verify that the proposed method can achieve almost the same performance as
linear online MPC with much lower online computational complexity and use less
fuel than LQR method.
