Model-based process control using nonconvex optimization

Over the past three decades, Model Predictive Control (MPC) has emerged as one of the most capable industrial control techniques available. The multivariable model-based control scheme relies on the online solution of an optimization problem to provide the optimal control sequence that minimizes the difference between the desired and model-predicted process operation over some horizon. Initially, MPC was a purely linear technique involving only continuous variables. The resulting optimization problem was convex and tractable for reasonably sized systems using the computing resources available at the time. However, strides in computing power and the development of efficient solvers allow for more complex formulations that can increase the utility of MPC.;The use of nonconvex optimization in advanced model-based control is theoretically advantageous in a number of contexts. Through the introduction of binary variables and use of propositional logic, control objective prioritization can be achieved. Similarly, hybrid dynamic systems that are characterized by discrete switching between multiple regimes of operation can be accommodated. These approaches require the solution of a nonconvex mixed-integer program. Chemical processes can also be sufficiently nonlinear to motivate the use of nonlinear models. This requires the solution of a nonconvex nonlinear program (NLP). The combination of binary variables with logic constraints and nonlinearity requires the solution of an extremely difficult nonconvex mixed-integer program (MINLP).;This work presents a number of MPC algorithms that focus on determining the global optimum as the controllers rely on the solution of nonconvex optimization problems. Local gradient-based methods can be used; however, these methods leave one susceptible to suboptimal local minima. In an attempt to address the nonconvex problem in a more global fashion, stochastic methods can be employed. These methods rely on probabilistic arguments for convergence to global optimality. For a particular class of problems, deterministic methods are employed which can rigorously guarantee global optimality.;The series of studies demonstrates the viability of each algorithm for use in real-time and details the solution strategies employed. If real-time constraints prevent convergence, problem simplification or reformulation is considered and fallback methods are in place. Both closed-loop performance and stability associated with each approach are addressed.