Control of cascading failures in coupled map lattices based on adaptive predictive pinning control

An adaptive predictive pinning control is proposed to suppress the cascade in coupled map lattices （CMLs）. Two monitoring strategies are applied： （1） A specific fraction of nodes with the highest degree or betweenness are chosen to constitute the set of monitored nodes; （2） During the cascade, an adaptive pinning control is implemented, in which only the nodes in the monitored set whose current state is normal but whose predictive state is abnormal, are pinned with the predictive controller. Simulations show that for the scale-free （SF） CML the degree-based monitoring strategy is advantageous over the betweenness- based strategy, while for the small-world （SW） CML the situation is the opposite. With the adaptive predictive pinning control, the fewer local controllers can effectively suppress the cascade throughout the whole network.