Lagrangian solution methods for nonlinear model predictive control

This work presents a simultaneous approach to the solution of the receding horizon, open-loop optimal model predictive control law for nonlinear systems using first-order Lagrangian methods. The nonlinear model considered is a general form of the initial value advective-diffusion parabolic partial differential equation. Others forms may be considered in a similar manner. The Lagrangian is formed from the discretized objective function, model and constraint equations. A finite volume approach is used to discretize the partial differential model equations. Inequality constraints on the model states and control inputs are handled with an active set method. The nonlinear equations resulting from the first order necessary conditions are then solved directly using a Newton-Krylov technique.