Generalized quasi-spectral model predictive static programming method using Gaussian quadrature collocation

A new generalized quasi-spectral model predictive static programming (GS-MPSP) method is proposed to efficiently solve a class of terminal-constrained optimal control problems with specified or free terminal time. A spectral representation method is used to model the profile of the control vector, then an infinite-dimensional optimization problem in a continuous-time framework is transformed into a small-dimensional static programming problem minimizing a certain performance index. Using the Gauss quadrature collocation method, the computation of the sensitivity matrix can be converted to the solution of a group of linear equations and algebraic summation at a few collocation nodes. Subsequently, the spectral coefficients and terminal time are efficiently obtained to eliminate terminal output deviations by solving the static programming problem. A simulation case with a scenario of intercepting a high-speed target with a specified impact angle in the midcourse phase was conducted. The results indicate that the proposed GS-MPSP approach has increased computational efficiency compared to traditional methods.