Indirect Hp-pseudospectral Method for Nonlinear Quadratic Optimal Control Problem

The nonlinear quadratic optimal control problem solving by general indirect pseudospectral method spents unnecessary calculation time, since there is the constant number of collocation points in process of the resulting two-point boundary value problem (TPBVP) discretization. In this paper, the indirect hp-pseudospectral method (IHPPM) for approximating the solution to nonlinear quadratic optimal problem is proposed. The quasi-linearization method is firstly used to linearize mathematical model. The nonlinear quadratic optimal problem on finite horizon is formulated. Secondly, the IHPPM is designed to solve the resultant optimal control problem. This novel method introduces adaptive hp-pseudospectral method with an indirect collocation technique. The IHPPM can be used to approximate the equation of TPBVP, derived from the Pontryagin's minimum principle and necessary conditions, to a system of algebraic equations. Because of simple matrix operations in the process of calculation and adaptive strategy, the probelm can be computed rapidly and efficiently. Simulation results about a spacecraft attitude maneuver optimal control problem verify the effectiveness of the proposed algorithm and feasibility of the controller.