Cluster synchronization of fractional-order complex networks via uncertainty and disturbance estimator-based modified repetitive control

The combined problems of cluster synchronization and disturbance rejection for a family of fractionalorder complex networks subject to coupling delay, unknown uncertainty and disturbances (UDs) are examined in this study. In particular, the existence of coupling delay is taken into the account with both known and unknown cases. First, a new uncertainty and disturbance estimator (UDE)-based control protocol is formulated for the concerned system to estimate and compensate for the effects of UD. Although the UDE strategy has proven to be a viable tool to deal with slowly changing UDs in control design, the presence of rapidly changing UDs or sinusoidal disturbances is not an effective tool. A well-known modified iterative control (MRC) block is built internally in a closed feedback control loop to solve this problem. After implementing UDE and MRC blocks into the feedback loop, the resulting system becomes almost UD-free. Moreover, a set of sufficient linear matrix inequality constraints are established to ensure the cluster synchronization of the resulting system. Lastly, the benefits, feasibility and robustness of the established UDE-based MRC scheme are confirmed by two illustrative examples. (c) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This study investigated the cluster synchronization and disturbance rejection for a family of fractional-order complex networks under coupling delay, unknown uncertainty, and disturbances. A new uncertainty and disturbance estimator-based control protocol was formulated, along with a modified iterative control block, to effectively handle rapidly changing disturbances and achieve nearly disturbance-free systems. Sufficient linear matrix inequality constraints were established to ensure cluster synchronization, and the benefits and robustness of the proposed scheme were confirmed through illustrative examples.