Robustness of Model Predictive Control to (Large) Discrete Disturbances

Abstract In recent years, theoretical results for model predictive control (MPC) have been expanded to address discrete actuators (decisions) and high-level planning and scheduling problems. The application of MPC-style methods to scheduling problems has been driven, in part, by the robustness afforded by feedback. The ability of MPC, and feedback methods in general, to reject small persistent disturbances is well-recognized. In many planning and scheduling applications, however, we must also consider an additional class of discrete and infrequent disturbances, such as breakdowns and unplanned maintenance. In this paper, we establish that nominal MPC is robust, in a stochastic context, to this class of discrete and infrequent disturbances. We illustrate these results with a nonlinear blending example.

[1]  Jifeng Zhang,et al.  A notion of stochastic input-to-state stability and its application to stability of cascaded stochastic nonlinear systems , 2008 .

[2]  P. Florchinger.  Lyapunov-Like Techniques for Stochastic Stability , 1995 .

[3]  David Angeli,et al.  Economic optimization using model predictive control with a terminal cost , 2011, Annu. Rev. Control..

[4]  T. Başar,et al.  Stochastic stability of singularly perturbed nonlinear systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[5]  Andrew R. Teel,et al.  Examples when nonlinear model predictive control is nonrobust , 2004, Autom..

[6]  James B. Rawlings,et al.  On the inherent robustness of optimal and suboptimal nonlinear MPC , 2017, Syst. Control. Lett..

[7]  James B. Rawlings,et al.  Model predictive control with discrete actuators: Theory and application , 2017, Autom..

[8]  Frank Allgöwer,et al.  Inherent robustness properties of quasi-infinite horizon nonlinear model predictive control , 2014, Autom..

[9]  Stephen J. Wright,et al.  Conditions under which suboptimal nonlinear MPC is inherently robust , 2011, Syst. Control. Lett..

[10]  Andrew R. Teel,et al.  A Matrosov Theorem for Adversarial Markov Decision Processes , 2013, IEEE Transactions on Automatic Control.

[11]  J. Tsinias.  Stochastic input-to-state stability and applications to global feedback stabilization , 1998 .

[12]  João Pedro Hespanha,et al.  Stochastic difference inclusions: Results on recurrence and asymptotic stability in probability , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).