Robust Model Predictive Control for Process Control and Supply Chain Optimization

Abstract

<p>Model Predictive Control (MPC) is traditionally designed assuming no model mismatch and tuned to provide acceptable behavior when mismatch occurs. This thesis extends the MPC design to account for explicit mismatch in the control and optimization of a wide range of uncertain dynamic systems with feedback, such as in process control and supply chain optimization.</p> <p>The major contribution of the thesis is the development of a new MPC method for robust performance, which offers a general framework to optimize the uncertain system behavior in the closed-loop subject to hard bounds on manipulated variables and soft bounds on controlled variables. This framework includes the explicit handling of correlated, time-varying or time-invariant, parametric uncertainty appearing externally (in demands and disturbances) and internally (in plant/model mismatch) to the control system. In addition, the uncertainty in state estimation is accounted for in the controller.</p> <p> For efficient and reliable real-time solution, the bilevel stochastic optimization formulation of the robust MPC method is approximated by a limited number of (convex) Second Order Cone Programming (SOCP) problems with an industry-proven heuristic and the classical chance-constrained programming technique. A closed-loop uncertainty characterization method is also developed which improves real-time tractability by performing intensive calculations off-line.</p> <p>The new robust MPC method is extended for process control problems by integrating a robust steady-state optimization method addressing closed-loop uncertainty. In addition, the objective function for trajectory optimization can be formulated as nominal or expected dynamic performance. Finally, the method is formulated in deviation variables to correctly estimate time-invariant uncertainty.</p> <p>The new robust MPC method is also tailored for supply chain optimization, which is demonstrated through a typical industrial supply chain optimization problem. The robust MPC optimizes scenario-specific safety stock levels while satisfying customer demands for time-varying systems with uncertainty in demand, manufacturing and transportation. Complexity analysis and computational study results demonstrate that the robust MPC solution times increase with system scale moderately, and the method does not suffer from the curse of dimensionality.</p>