Algebraic polynomials are used to approximate the state trajectory, the control and the functions in differential equations and in the criterion for the constrained optimal cyclic control problem. Several discretized problems using algebraic polynomials are proposed to approximate the basic control problem. Sufficient conditions for the convergence of solutions of approximating problems to the optimal solution of the basic problem are given and the convergence rate is estimated. The application to a class of industrial optimal cyclic control problems is discussed.