Lavrentiev Phenomenon in hp Gaussian Quadrature Collocation Methods for Optimal Control

摘要

Lavrentiev phenomenon in the numerical solution of optimal control problems of hp Gaussian quadrature collocation is studied. The nonlinear programming problem that arises from the standard Legendre-Gauss-Radau collocation method is modified to include constraints that prevent Lavrentiev phenomenon from occurring. This new formulation of the Legendre-Gauss-Radau collocation method is applied to an optimal control problem whose optimal solution has a control discontinuity. The results obtained by including the Lavrentiev constraints show a significant improvement in the the accuracy of the solution when compared with the standard Legendre-Gauss-Radau collocation method.