Synchronization optimization of networked second order infinite dimensional systems

We consider optimization aspects for the synchronization control of networked second order infinite dimensional systems. It is assumed that a number of identical such systems are desired to be synchronized and using output feedback controllers, the resulting coupled systems are brought in an aggregate form in order to optimize the synchronization gains. Using a closed-loop energy as the optimization metric, the choice of the synchronization gains reduces to the minimization of the optimization index. This eventually is described by the trace of the solution to a parameterized Lyapunov operator equation. Numerical studies on a network of four one-dimensional cantilevered beams provide insight on the optimization of the proposed synchronization control.