,In this thesis, in addition to introducing the orthogonal triangular functions we show that they are a characterization of the well-known piecewise linear polynomials which the orthogonality of them is derived. We then deliberate their corporeity and obtain integral and product operational matrices. Then by using the triangular functions we solve the multinomial nonlinear optimization control problems. The main aim of this method is changing the optimal control problem into linear or nonlinear algebraic systems that the solution is so easy. Also at this thesis, we study the main problem in Van der pol and rigid asymmetric spacecraft problems and Duffing nonlinear oscillator which are very important in Control and Systems Theory.