Adaptive Learning Control for Nonlinearly Parameterized Systems with Periodically Time-varying Delays
周期时变时滞非线性参数化系统的自适应学习控制

An adaptive learning control scheme is designed for first-order nonlinearly parameterized systems with unknown pe- riodically time-varying delays.It is assumed that the common periodicity of unknown time-varying parameter,time-varying delay,and reference signal are known. By reconstructing the system equation,all unknown time-varying terms including the time-varying delay are combined into a periodically time-varying vector which is estimated by a periodic adaptation mechanism. By constructing a Lyapunov-Krasovskii-like composite energy function,we prove the boundedness of all signals and the con- vergence of tracking error.The results are extended to a class of high-order nonlinear systems with mixed parameters.Two simulation examples are provided to illustrate the effectiveness of the control algorithms proposed in this paper.