Numerical Solution of Bang-Bang and Singular Optimal Control Problems Using Integral Legendre-Gauss-Lobatto Collocation

A method for solving bang-bang and singular optimal control problems using the integral form of Legendre-Gauss-Lobatto collocation is developed. The optimal control problem is developed in multiple-phase form in order to accurately capture discontinuities in the control. This multiple-phase optimal control problem is approximated using a recently developed integral form of Legendre-Gauss-Lobatto (LGL-I) collocation method, where the LGL-I method has the key feature that it approximates the state and control at both endpoints of the interval. In addition, recent research has shown that this new LGL-I method is a partitioned Runge-Kutta method that exhibits superconvergence at the mesh points. The method developed in this paper is applied to a minimum-time axisymmetric reorientation problem with bang-bang and singular control structure, where it is found that the LGL-I method produces accurate solutions.