Discrete time model predictive control design using Laguerre functions

In the design of model predictive controller (MPC), the traditional approach of expanding the projected control signal uses the forward operator to obtain the linear-in-the-parameters relation for predicted output. In this paper, by using a performance specification on the exponential change rate of the projected control signal, a more appropriate expansion, related to Laguerre networks, is introduced. It is shown that the number of terms used in the optimization procedure can be reduced to a fraction of that required by the usual procedure in the case of rapid sampling, and as a result, the numerical condition of the optimization algorithm can be significantly improved. Furthermore, the proposed algorithm is easy to tune for closed-loop performance with two explicit tuning parameters. By relaxing the constraint on the exponential change rate of the control signal and allowing arbitrary complexity in describing the trajectory, the proposed approach becomes equivalent to the traditional approach in MPC design.