Inherent Stochastic Robustness of Model Predictive Control to Large and Infrequent Disturbances

We introduce a new class of large, infrequent disturbances to complement the small, persistent disturbances typically considered in robustness analysis. This new class of disturbances includes discrete disturbances that become pertinent when considering discrete actuators and production scheduling in control problems. To properly account for the infrequent nature of these disturbances, we define a stochastic form of robustness. Under suitable assumptions, we prove that certain closed-loop systems subject to large, infrequent disturbances admit an SISS-Lyapunov function and are robust in this stochastic context. We apply these results to economic model predictive control (MPC) with a strictly dissipative nominal system and stage cost, which includes tracking MPC as a special case, and prove that economic MPC is robust to large, infrequent disturbances. Without dissipativity assumptions, we define and establish robust asymptotic performance for economic MPC. We present a simple tracking problem to illustrate the results of this work, and a production scheduling (economic MPC) problem, to demonstrate the relevance of this analysis to practical applications.