Iterative learning control algorithm based on Chebyshev orthonormal basis for nonlinear systems

A new iterative learning control algorithm with global convergence for nonlinear systems is presented. Constructed Chebyshev orthornormal polynomial basis in the control space, the iterative learning control problem is transformed as the optimization problem. The iterative projection method is utilized to solve this problem so that the new iterative learning control law is derived. Based on the extension method, a new algorithm with global convergence for nonlinear iterative learning systems is developed. Sufficient conditions of convergence of this approach are given and the global convergence is proved. Such an algorithm has the advantage of the simple computation and arbitrarily chosen initial control.