On-line reentry trajectory optimization of hypersonic vehicle based on improved Gauss pseudospectral method

The improved Gauss pseudospectral method (IGPM) with the linear final state constraint is proposed to solve the Bolza problem. The Bolza problem is disrcetized into the nonlinear programming problem (NLP) by the approximations of the state and the costate at the Legendre-Gauss (LG) points and the boundary points. The differential of the state can be expressed as the linear combination of the states at the discrete points approximately. Therefore, the dynamic equations can be transformed into the algebraic equations and the cost is also expressed as the function of the state and the control. The costate mapping theorem is derived to compute the costate directly. The methods to compute the initial costate and the boundary controls are given for completing the IGPM. The NLP is solved by the sequential quadratic programming method. It is easy to check the optimality of the solution. The proposed method is utilized to solve the the reentry trajectory optimization problem of the hypersonic vehicle. The results shown that the The computer time for solving the problem is about 3 seconds. Therefore, this method can be used to generate the optimal trajectory of the hypersonic vehicle on line.