Non-linear prediction horizon time-discretization for model predictive control of linear sampled-data systems

Model predictive sampled-data control of linear continuous-time plants is considered. The time-discretization of the prediction horizon may be non-linear, in order to reduce the number of optimization variables for a given prediction horizon length. This is done for the purpose of allowing faster implementation. While the method is aimed at constrained systems, this paper focuses on the achievable performance of such control strategies for unconstrained systems. A general solution to the finite-horizon optimal control problem is derived for a prediction horizon of arbitrary time-discretization. The model predictive control strategy is consequently derived, and the optimal control input shown to be given by a time-invariant state feedback expression. Three non-linear prediction horizon time-discretization schemes are proposed, and their relative merits discussed. The benefit of employing the presented control strategy is demonstrated by a satellite attitude control case study. The same case study is further used to highlight limitations of and performance differences between the three proposed prediction horizon time-discretization schemes.