<i>H</i>∞Synchronization Control for Multitiered Networked Re-Entrant Manufacturing Systems

In this article, robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synchronization problem for a class of networked re-entrant manufacturing systems (RMSs) is investigated by utilizing state feedback control and distributed adaptive state feedback control approaches. Different from the isolated single re-entrant manufacturing line, a networked RMS with three-tiered architecture is presented, which contains the production line, the production workshop and the workshop network. Based on the mass conservation law, the dynamics of the production line and the production workshop are established by a first-order linear hyperbolic PDE and a first-order semi-linear hyperbolic PDE, respectively. On one hand, in view of communication delays and external disturbances that might exist in the system, a delayed state feedback controller is constructed to address robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synchronization of the networked RMSs. On the other hand, considering the uncertainty with coupling gain and the unavailability of global information, a distributed cooperative controller with the edge-dependent adaptive gain is further developed to ensure robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synchronization of the networked RMSs. Numerical simulations validate the effectiveness of both proposed control schemes.