Preconditioning for continuation model predictive control
For practitioners of nonlinear model predictive control, this work offers a simpler preconditioning approach to speed up real-time optimization, though it is an incremental improvement over existing methods.
The paper simplifies the construction of preconditioners for the GMRES method in continuation NMPC by using approximate forward-backward recursions or reusing previous solutions, aiming to accelerate convergence.
Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) deals with nonlinear models and/or constraints. A Continuation/GMRES Method for NMPC, suggested by T. Ohtsuka in 2004, uses the GMRES iterative algorithm to solve a forward difference approximation $Ax=b$ of the original NMPC equations on every time step. We have previously proposed accelerating the GMRES and MINRES convergence by preconditioning the coefficient matrix $A$. We now suggest simplifying the construction of the preconditioner, by approximately solving a forward recursion for the state and a backward recursion for the costate, or simply reusing previously computed solutions.