A real‐time algorithm for nonlinear receding horizon control using multiple shooting and continuation/Krylov method

In this paper, we propose a real‐time algorithm for nonlinear receding horizon control using multiple shooting and the continuation/GMRES method. Multiple shooting is expected to improve numerical accuracy in calculations for solving boundary value problems. The continuation method is combined with a Krylov subspace method, GMRES, to update unknown quantities by solving a linear equation. At the same time, we apply condensing, which reduces the size of the linear equation, to speed up numerical calculations. A numerical example shows that both numerical accuracy and computational speed improve using the proposed algorithm by combining multiple shooting with condensing.