Learning control for bilinear parametric systems with time-varying delays and time-varying control gains

A learning control scheme is designed for first-order bilinear parametric systems with unknown periodically 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, the time-varying delay is combined into a periodically time-varying vector which is estimated by a periodic adaptation mechanism. By constructing a Lyapunov-Krasovskii energy function, we prove the boundedness of all signals and the convergence of tracking error. A simulation example is provided to illustrate the electiveness of the control algorithms proposed in this paper.