Optimal tracking performance limitation of networked control systems with periodic signal reference input based on power spectrum

Abstract

This paper studies the tracking problem for LTI SISO discrete-time networked control systems with periodic signal reference input. The most important difference from the existing works on the tracking problem is that the reference input signal considered in this study is not the common non-periodic signal (e.g., a step signal) considered in most of the existing works, but a discrete-time periodic signal, whose waveform shapes is the same and repeated in each period, accordingly, the power of input signal in each period is fixed. So we study the system response to the power of input signal based on power spectrum. The tracking performance is measured by the power of the tracking error between the plant output and the reference, and the optimal tracking performance is thus measured by the mean power of the tracking error. In the networked control systems under consideration, packet dropouts may be only existed in the forward communication channel, and the packet dropouts may be viewed as a mixture of deterministic signal and stochastic signal, thus the error caused by packet dropouts is assumed to be a product of the original signal and a white noise. By applying Parseval identity and Wiener-Khinchin theorem as well as norm matrix theory, the lower bound of the performance in tracking is derived in terms of the characteristics of the plant and the uncertain type of the signal.