Adaptive Sliding Mode Synchronous Control for Complex Networks With Amplify-and-Forward Relays

This paper aims to the remote synchronous control for complex networks with amplify-and-forward (AF) relays. Firstly, the AF relay dynamic with random noise is integrated into the control signal transmission. Secondly, the complex networks incorporating an AF relay is converted into the sliding control mode (SMC), which robustly addresses unknown disturbances among the nodes to achieve synchronous states. Thirdly, an adaptive gain mechanism based on the equivalent value of sign function of SMC is proposed to estimate the disturbance amplitude, hence mitigating the chattering of SMC. Finally, the illustrative simulation demonstrated the effectiveness of proposed methodology. Note to Practitioners—This paper is motivated by the synchronous control of the hydraulic supports in underground coal mining, where hundreds of hydraulic supports form a complex network, often with the centralized controller situated remotely from emulsion pump station. In actual engineering application, the incorporation of amplify-and-forward (AF) relays in the control signal transmission process is advisable. However, the AF relays would introduce noise and exacerbates system uncertainty. Consequently, the primary objective of this paper is to design a robust controller tailored for this complex network with AF relays. The existing research seldom addresses this particular challenge. To tackle this issue, this paper design a sliding mode controller (SMC). Within the framework of SMC, the transmission and AF relaying processes are transformed into a sliding variable dynamic; an adaptive mechanism for sign function is proposed to mitigate the SMC chattering. We mathematically prove the reachability of the sliding mode, the asymptotic stability of the control system, and the convergence of the adaptive gain. Preliminary simulation experiments demonstrate the effectiveness of our proposed methodology. In future research, we aim to address the constraint faced by some transmission channels of AF relays in the synchronous control of complex networks.