Chebyshev Finite Difference Method for Solving Constrained Quadratic Optimal Control Problems

In this paper the Chebyshev finite difference method is employed for finding the approximate solution of time varying constrained optimal control problems. This approach consists of reducing the optimal control problem to a nonlinear mathematical programming problem. To this end, the collocation points (Chebyshev Gauss-Lobatto nodes) are introduced then the state and control variables are approximated using special Chebyshev series with unknown parameters. The performance index is parameterized and the system dynamics and constraints are then replaced with a set of algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the technique.