Desynchronization and resynchronization of networked second order finite and infinite dimensional systems

This work considers the synchronization of interconnected second order infinite dimensional systems. An output feedback based synchronization controller is designed in order to enhance a measure of synchronization amongst the infinite dimensional systems and when using the aggregate form of the networked systems, the choice of the optimal gains in the synchronization controllers reduces to the optimization of an associated quadratic index. A desynchronization action which takes the form of severing a link between any two connected systems is interpreted as a benign action which results in a delayed synchronization or convergence of the synchronization measure to a nonzero value. When the desynchronization action takes the form of sign reversal of a link between two connected systems, it is interpreted as a malicious adversarial action and which results in destabilization of the networked systems with an unbounded synchronization measure. The desynchronization action is viewed as a fault occurring in the networked system and an adaptive scheme is thus used to monitor these interconnected systems in order to detect the presence of the desynchronization action. In order to maintain the synchronization of the interconnected systems, an adaptive fault accommodating scheme is proposed which takes the form of control reconfiguration and which ensures the resynchronization of the interconnected systems. Both finite and infinite second order systems are considered and a numerical example with four interconnected cable PDEs is included to demonstrate the effectiveness of the desynchronization monitoring scheme and the subsequent resynchronization policy.