Direct Trajectory Optimization and Costate Estimation of State Inequality Path-Constrained Optimal Control Problems Using a Radau Pseudospectral Method

A Radau pseudospectral method is derived for solving state-inequality path constrained optimal control problems. The continuous-time state-inequality path constrained optimal control problem is modified by applying a set of tangency conditions at the entrance of the activity of the path constraint. It is shown that the first-order optimality condition of the nonlinear programming problem associated with the Radau pseudospectral method is equivalent to the Radau pseudospectral discretized first-order optimality conditions of the modified continuous-time optimal control problem. The method is applied to a classical state-inequality path constrained optimal control problem and it is found that the solution accuracy is improved significantly when compared with the accuracy of the solution obtained using the original Radau pseudospectral discretization.