AILC of Parameterized Nonlinear Time-Delay Systems

In this chapter, based on a deep investigation of research results concerning nonlinear systems with time-delay and dead-zone, a new AILC scheme is proposed for a class of nonlinear time-varying systems with unknown time-varying time-delays and unknown input dead-zone nonlinearity running on a finite time interval repetitively. Firstly, a novel representation with time-varying slope for the dead-zone nonlinearity characteristic is built, this model for dead-zone is very simple in form and broadly representative. Using appropriate Lyapunov-Krasovskii functional in the Lyapunov function candidate, the uncertainties from unknown time-varying delays are removed such that control law is delay-independent. The identical initial condition for ILC has been relaxed by introducing the boundary layer function. The hyperbolic tangent function is employed to avoid the possible singularity problem, which guarantee the continuity of control signal. Theoretical analysis by constructing Lyapunov-like CEF has shown that the tracking errors converge to a small residual domain around the origin as iteration goes to infinity. At the same time, all the closed-loop signals remain bounded. Simulation results have been provided to show the effectiveness the proposed control scheme and the advantage in tackling this kind systems compared with traditional adaptive control method.