A Sequential Quadratic Programming Method for Nonlinear Model Predictive Control

Abstract

A local sequential quadratic programming, or Newton-Lagrange, approach to the solution of the partial differential equation constrained optimization problem arising from the application of model predictive control on nonlinear distributed parameter systems is presented. The nonlinear system model considered is a general form of the initial value advective-diffusion parabolic partial differential equation. This equation form is chosen because it describes a wide range of chemical process systems, however, other initial value partial differential equation forms can be considered in a similar manner. The optimization problem is constructed from the discretized model, constraint, and objective function equations. A finite volume approach is used to discretize the distributed parameter model equat ions. Inequality constraints on the model states and controls are addressed with an active set method. The nonlinear equations resulting from the first order Karush-Kuhn-Tucker conditions are solved directly using preconditioned Newton-Krylov techniques.