Performance measures in model predictive control with non-linear prediction horizon time-discretization

Model predictive sampled-data control of constrained, linear, time-invariant, continuous-time plants is considered. The time-discretization of the prediction horizon may be non-linear, in order to reduce the computational complexity of online MPC methods by lowering the number of optimization variables for a given prediction horizon length. The main contribution of this paper is to propose two closed-loop performance measures in order to evaluate the salient performance properties of non-linearly time-discretized prediction horizons. A numerical motivating example comparing two prediction horizon time-discretizations with an order of magnitude difference in the number of optimization variables is discussed, and subsequently the results of a sensitivity analysis of the two proposed performance measures with respect to the prediction horizon time-discretization are presented. The use of non-linearly time-discretized prediction horizons is also shown to be relevant for complexity reduction in offline MPC strategies.