Fractional-order iterative learning control and identification for fractional-order Hammerstein system

The fractional-order Hammerstein system is a cascading system composed of a static nonlinearity followed by a fractional-order linear dynamics, which is a typical nonlinear system satisfying the local Lipschitz condition, and exhibits quasi-linear properties. This paper combines the fractional-order iterative learning control (FOILC) and the fractional-order iterative learning identification (FOILI), which is applied to the perfect tracking control of fractional-order continuous Hammerstein systems. A novel order learning strategy is proposed to estimate the differentiation order accurately. A practical and robust identification based FOILC scheme is derived so that the convergence speed can be optimized accordingly. Two illustrated examples are provided to validate the above concepts.