Chebyshev Finite Difference Method for Solving Constrained Quadratic Optimal Control Problems

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