Preconditioning for continuation model predictive control

TL;DR

This paper improves the efficiency of solving nonlinear model predictive control problems by simplifying and reusing preconditioners in iterative solvers, enhancing convergence speed.

Contribution

It introduces a simplified preconditioning approach for the GMRES-based continuation method in NMPC, reducing computational complexity and improving convergence.

Findings

Preconditioning accelerates GMRES convergence in NMPC.

Reusing previous solutions simplifies preconditioner construction.

The method enhances real-time applicability of NMPC.

Abstract

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.