Double iterative optimal learning control of nonlinear repetitive motion system

In this work, a double iterative optimal learning control strategy is proposed for a nonlinear systems with non-parametric uncertainties and output constraints. Firstly, a class of saturated nonlinear functions is introduced, which can not only satisfy the position constraints of the system, but also ensure that the tracking error converges to the given neighborhood. Then, a reference trajectory self-tuning strategy is designed for the initial error of each iteration. A fixed adjustment time domain is set in each iteration cycle, and the reference trajectory of the next iteration is adjusted according to the output of the last iteration. The dual iterative control structure can update the parameters of the two iterative controllers at the same time to deal with the non-parametric uncertainties of the system. Furthermore, the convergence and stability of the double iterative control strategy are proved by using the barrier composite energy function. Finally, an example is given to prove the effectiveness of the control strategy. © 2021, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.