Nonlinear receding horizon control via singular value decomposition with error correction method for singular vectors and singular values

Nonlinear receding horizon control (NRHC) attracts much attention in recent years. For NRHC, C/GMRES proposed by Otsuka is one of the most effective methods. Generalized minimal residual method (GMRES) is employed in C/GMRES, however, GMRES may become numerically unstable under some conditions in the sense of numerical calculation. This results in instability of the controlled system in the sense of the theory of differential equations. In this paper, we propose a new NRHC control method via singular value decomposition (SVD) with modified discrete Lotka-Volterra algorithm with shift (mdLVs). For singular vector computation in SVD, we propose a new method called `simultaneous error correction method.' The proposed method achieves high precision, numerical stability, and low computational cost. We show computer simulation results of asymptotic stabilization of an inverted pendulum with the proposed method and confirm the effectiveness through a comparison with C/GMRES.