Continuity and Monotonicity of the MPC Value Function with respect to Sampling Time and Prediction Horizon - Bachtiar,V; Kerrigan,EC; Moase,WH; Manzie,C (Automatica, 2015)
The digital implementation of model predictive control (MPC) is fundamentally governed by two design parameters; samplingtime and prediction horizon. Knowledge of the properties of the value function with respect to the parameters can be used fordeveloping optimisation tools to find optimal system designs. In particular, these properties are continuity and monotonicity.This paper presents analytical results to reveal the smoothness properties of the MPC value function in open- and closed-loopfor constrained linear systems. Continuity of the value function and its differentiability for a given number of prediction stepsare proven mathematically and confirmed with numerical results. Non-monotonicity is shown from the ensuing numericalinvestigation. It is shown that increasing sampling rate and/or prediction horizon does not always lead to an improved closedloopperformance, particularly at faster sampling rates.