Preconditioning for continuation model predictive control

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 coeffcient 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.