Lunar soft landing trajectory optimization by a Chebyshev pseudospectral method

The optimization of lunar soft landing trajectory is an optimization control problem with non-linear free terminal time and control constrained.. The application of the Chebyshev pseudospectral is described on the optimal control problems. This method employs Nth Lagrange polynomial approximations for the state and control variables to transform the state differential equations to algebraic equations. Finally the optimal control problem is transformed to a nonlinear programming problem. In process of solving the optimal control problem using matlab, control variables and flying time are used as optimal variables. Simulation results demonstrate the methodology for the optimal trajectory designing has strong convergence.