(140e) A Predictive Control Method for Nonlinear Transport-Reaction Processes

An important research area that has received a lot of attention in the past decade is controller design for distributed processes, mathematically modeled by nonlinear parabolic partial differential equation (PDE) systems. One of the research directions involves the development of methods for controller design based on reduced-order models (e.g., obtained using linear or nonlinear Galerkin's methods) that capture the dominant dynamics of the process and can be solved numerically in real time. An important issue however that is not explicitly addressed is the presence of constraints in the process operation.

State & input constraints are widely prevalent in current industrial practice which has motivated a need for controller design methodologies which explicitly address these process constraints. Model predictive control (MPC), also known as receding horizon control, is one such powerful tool for handling these process constraints with an optimal control setting. The control action in MPC is calculated by solving repeatedly, online, a finite-horizon open-loop optimization problem at each sampling time. As the control action is computed online during process evolution, MPC has the capabilities to suppress the external disturbances and tolerate model inaccuracies (using feedback control) during the course of forcing the system to follow certain optimal path that respects the process constraints.

The main focus of the manuscript lies in the development of a computationally efficient method to identify the optimal control action with respect to predefined performance criteria. The optimal control problem is formulated as a receding control horizon one, thus necessitating the solution of a dynamic optimization problem at each time step. Employing nonlinear transformations and assuming piece-wise constant control action, the dynamic optimization problem is reformulated as a nonlinear optimization one with analytically computed sensitivities. This allows for the problem solution using standard, gradient-based, search algorithms. The proposed method lies at the interface between collocation and shooting methods, since the distributed states are discretized explicitly in space and time and their sensitivity to the control action is analytically computed, reminiscent of collocation methods, while the states now enter the optimization problem explicitly as a nonlinear function of the control action and are eliminated from the equality constraints, thus reducing the number variables, evocative of shooting methods.