Design and optimization of synchronization controllers for networked second order infinite dimensional systems

This work considers a class of second order infinite dimensional parameter systems that often model flexible structures and it is assumed that a number of identical such systems are desired to be synchronized. Using output feedback controllers, the resulting coupled systems are brought in an aggregate form that is conducive to optimization of the synchronization gains. Using the closed-loop energy as a suitable optimization index, the choice of the synchronization reduces to the minimization of the optimization index, which eventually is described by the trace of the solution to a parameterized Lyapunov operator equation. Extensive numerical studies on a network of four one-dimensional cantilevered beams provides further insight on the synchronization control.