Numerical Methods for Solving Linear Time Varying Quadratic Optimal Control Problems

Abstract

In this article, we discussed linear time varying optimal control problems with quadratic performance index, and approximated control variable, state variable and performance index. There are many different numerical processes for approximating of linear time varying quadratic optimal control problem. Two of those are explained here the Legendre scaling function and Chebyshev scaling function methods using the MATLAB. The methods will be explained, and then applied to test problems to see how they perform. The results show that the Legendre scaling function was the best of the Chebyshev scaling function methods being a computation. Hence, the Legendre scaling function method is more suitable for solving the linear time varying quadratic optimal control systems.

Keywords

• Optimal control problems
• Legendre scaling function
• Chebyshev scaling function
• State variable
• Control variable