UC Santa Barbara

Uncertainty is inherent to all science and engineering models. Any algorithm proposed to design, schedule, or control an industrial process must therefore be robust, i.e., the algorithm must be able to withstand and overcome this uncertainty. In this dissertation, we focus specifically on model predictive control (MPC), the advanced control algorithm of choice for chemical process control with a growing list of applications in several other engineering disciplines as well. For deterministic descriptions of this uncertainty, MPC is known to be robust to sufficiently small disturbances. This robustness is afforded by feedback and does not require any characterization of this uncertainty within the control algorithm.

Stochastic descriptions of uncertainty, however, are often better suited to model the behavior of physical systems and have proven highly useful in a variety of science and engineering applications. To that end, we expand the theory of robustness for MPC to address these stochastic descriptions of uncertainty and establish that MPC is robust in this stochastic context. We then apply this theory to the emerging field of stochastic MPC (SMPC), in which a stochastic model of this uncertainty is used directly in the control algorithm. Through the concept of distributional robustness, we further establish that SMPC is robust to uncertainty within even the stochastic model used in the control algorithm. This result in fact unifies the analysis of both MPC and SMPC, thereby allowing a novel comparison of the theoretical properties afforded by these two algorithms. We also demonstrate via suitable examples that including stochastic information in a control algorithm is not always beneficial to the controller's performance. In the second part of this dissertation, we consider the stochastic robustness of MPC to a new class of large and infrequent disturbances, motivated by recent applications of MPC to production planning and scheduling problems. Using these results and the MPC framework, we then design a closed-loop scheduling algorithm that is robust to the large and infrequent disturbances pertinent to production scheduling problems. This algorithm is further modified to address computational and practical limitations and is therefore suitable for large-scale production scheduling applications.