Triangular Orthogonal Functions for Nonlinear Constrained Optimal Control Problems

This study presents a numerical method for solving nonlinear optimal control problems including terminal state constraints, state and control inequality constraints. The method is based on Triangular Orthogonal Functions (TFs). By approximating the dynamic systems, performance index and boundary conditions into triangular orthogonal series, the optimal control problem is converted into algebraic equations with unknown coefficients. Then the problem can be easily solved by some iterative method. Illustrative examples are included to demonstrate the accuracy and applicability of the presented method.