Direct Trajectory Optimization by a Chebyshev Pseudospectral Method

We present a Chebyshev pseudospectral method for directly solving a generic Bolza optimal control problem with state and control constraints. This method employs Nth-degree Lagrange polynomial approximations for the state and control variables with the values of these variables at the Chebyshev-Gauss-Lobatto (CGL) points as the expansion coefficients. This process yields a nonlinear programming problem (NLP) with the state and control values at the CGL points as unknown NLP parameters. Numerical examples demonstrate that this method yields more accurate results than those obtained from the traditional collocation methods.