Continuation/GMRES method for fast algorithm of nonlinear receding horizon control

Proposes a fast algorithm for nonlinear receding horizon control. The control input is updated by a differential equation to trace the solution of an associated two-point boundary-value problem. A linear equation involved in the differential equation is solved by the generalized minimum residual (GMRES) method, one of the Krylov subspace methods, with Jacobians approximated by forward differences. The error in the entire algorithm is analyzed and is shown to be bounded under mild conditions. The proposed algorithm is applied to a two-link arm whose dynamics is highly nonlinear.