Attitude stabilization with actuators subject to switching-time constraints using explicit MPC

This paper is concerned with the design of an explicit model predictive controller (eMPC) for attitude stabilization using on-off thrusters subject to switching-time constraints. ¹²In the proposed approach, the control actions are specified by a sequence of integer values in the set {-1, 0, +1}, i.e the thrusters can be fully opened in one of two possible directions (-1 or +1) or remain closed (0). Switching-time constraints are taken into account by imposing restrictions on the minimum number of consecutive equal elements in the control sequence. The explicit solution to the constrained MPC problem is computed by solving a multi-parametric mixed integer linear program (mpMILP), where the parameters are the components of the state vector. The solution to the mpMILP is a piecewise affine (PWA) function, which can be evaluated at each sampling time to obtain the optimal control law. Since the on-line computation effort is restricted to a table-lookup, the controller can be implemented using a simple computational hardware.