Symplectic method based on generating function for receding horizon control of linear time-varying systems

A novel method for solving the linear receding-horizon control (RHC) problem with time-varying coefficients is proposed based on a generating function and the standard symplectic form of Hamiltonian systems. In contrast to other methods used to solve the linear RHC problem, the generating function is utilized to avoid directly online integrating the differential Riccati equation (DRE). Solutions to the DRE at discrete time points have been obtained by applying the generating function at each computation step. The derivation of the coefficient includes calculating the state transition matrices of the linear Hamiltonian system using the Magnus method, which preserves the symplectic structure of the Hamiltonian system. Numerical simulations of spacecraft rendezvous demonstrate that the proposed symplectic method obtains highly precise results for relatively long discretization sizes, and then yields computational efficiency improvements of one to two orders of magnitude compared with conventional backward sweep methods and the Legendre pseudospectral methods.