Repetitive learning control: existence of solution, convergence and robustification

In this paper, we propose a repetitive learning control (RLC), which deals with nonlinear dynamical systems with non-parametric uncertainties. We address three fundamental issues associated with the new learning control methods: the existence of the solution, learning convergence property and robustification, which are indispensable for the learning control methods to evolve to a new paradigm. Applying the existence theorem of the differential difference equation of neutral type, and using Lyapunov-Krasovskii functional, the existence of solution and the learning convergence can be proven rigorously. To enhance the robustness of the repetitive learning control, we further develop two kinds of robustification methods with projection and damping respectively to ensure the boundedness of the learning signals