Discrete-time adaptive learning control for parametric uncertainties with unknown periods

In this paper, we approach the problem of unknown periods for a class of discrete-time parametric nonlinear systems with nonlinearities which do not necessarily satisfy the sector-bounded condition. The unknown periods hide in the parametric uncertainties, which is difficult to estimate. By incorporating a logic-based switching mechanism, we estimate the period and bound of unknown parameter simultaneously under Lyapunov-based analysis. Rigorous proof is given to demonstrate that a finite number of switchings can guarantee the asymptotic regulation of the nonlinear system considered. The simulation result also shows the efficacy of the proposed switching periodic adaptive control method.