A continuation/GMRES method for fast computation of nonlinear receding horizon control

In this paper, a fast numerical algorithm for nonlinear receding horizon control is proposed. The control input is updated by a differential equation to trace the solution of an associated state-dependent two-point boundary-value problem. A linear equation involved in the differential equation is solved by the generalized minimum residual 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 some conditions. The proposed algorithm is applied to a two-link arm whose dynamics is highly nonlinear. Simulation results show that the proposed algorithm is faster than the conventional algorithms.