Abstract: In this paper, linear and nonlinear quadratic optimal control problems are solved by applying least square method based on Bernstein polynomials. We divide the interval which includes t , into k subintervals and approximate the trajectory and control functions by B {e}zier coefficients. We have chosen the Bernstein polynomials as piacewise polynomials of degree three, and determined Bernstein polynomials on any subinterval by four B {e}zier coefficients. By using least square method, we introduce an optimization problem and compute the B {e}zier coefficients by solving this optimization problem. Numerical experiments are presented to illustrate the proposed method.

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