Novel Adaptive Learning Control of Linear Systems with Completely Unknown Time Delays

A novel output-feedback adaptive learning control approach is developed for a class of linear time-delay systems. Three kinds of uncertainties: time delays, number of time delays, and system parameters are all assumed to be completely unknown, which is dfferent from the previous work. The design procedure includes two steps. First, according to the given periodic desired reference output and the allowed bound of tracking error, a suitable finite Fourier series expansion (FSE) is chosen as a practical reference output to be tracked. Second, by expressing the delayed practical reference output as a known time-varying vector multiplied by an unknown constant vector, we combine three kinds of uncertainties into an unknown constant vector and then estimate the vector by designing an adaptive law. By constructing a Lyapunov-Krasovskii functional, it is proved that the system output can asymptotically track the practical reference signal. An example is provided to illustrate the effectiveness of the control scheme developed in this paper.