This paper suggests a new and efficient method for solving linear quadratic optimal control problems. A shifted chebyshev matrix approach is implemented for solving this problem. In this method, the problem of optimal control changes into a problem of non-linear programming which can be solved easily.
The corresponding nonlinear programming problem will be solved using Matlab software to find the unknown coefficients which are related to the approximate solution. Numerical examples are also given in order to compare this new method with another one.