Computational Method for Optimal Guidance and Control Using Adaptive Gaussian Quadrature Collocation

Abstract

A method is described for computational optimal guidance and control using adaptive Gaussian quadrature collocation and sparse nonlinear programming. The method employs adaptive Legendre–Gauss–Radau (LGR) quadrature collocation using a mesh truncation and remapping procedure at the start of each guidance cycle, thereby retaining only the mesh points associated with the unexpired horizon. Using this approach, the starting mesh for a guidance cycle is smaller than the starting mesh used on the previous guidance cycle. The nonlinear programming problem is then solved on the reduced mesh corresponding to the unexpired horizon to generate the control that is used on the current guidance cycle. It is noted that the mesh points on the unexpired horizon are well placed for rapidly solving the LGR quadrature collocation approximation of the optimal control problem. The method developed in this paper is demonstrated on two challenging aerospace optimal control problems. For both examples, the dynamics are simulated on each guidance cycle using a perturbed dynamic model in the absence and presence of a computation time delay. The results of this study demonstrate that the method developed in this paper is viable as a computational method for optimal guidance and control.