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arXiv · 1509.02861

Preconditioning for continuation model predictive control

Andrew Knyazev·Alexander Malyshev
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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.

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Andrew Knyazev, Alexander Malyshev. 2015-09-09. Preconditioning for continuation model predictive control. https://doi.org/10.1016/j.ifacol.2015.11.282

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