Continuity and monotonicity of the MPC value function with respect to sampling time and prediction horizon

• Vincent Bachtiar ^[1] ; Eric C. Kerrigan ^[2] ; William H. Moase ^[1] ; Chris Manzie ^[1]
  1. [1] University of Melbourne

     University of Melbourne

     Australia

     
  2. [2] Imperial College London

     Imperial College London

     Reino Unido

     
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 63, 2016, págs. 330-337
• Idioma: inglés
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• Resumen

  • The digital implementation of model predictive control (MPC) is fundamentally governed by two design parameters; sampling time and prediction horizon. Knowledge of the properties of the value function with respect to the parameters can be used for developing optimization 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-loop for constrained linear systems. Continuity of the value function and its differentiability for a given number of prediction steps are proven mathematically and confirmed with numerical results. Non-monotonicity is shown from the ensuing numerical investigation. It is shown that increasing sampling rate and/or prediction horizon does not always lead to an improved closed-loop performance, particularly at faster sampling rates.