Adaptive output feedback synchronization of networked distributed parameter systems

The optimization and adaptation of the synchronization gains for a class of networked systems is presented in which the state of each of the networked nodes is governed by a distributed parameter system. The design objectives aim at ensuring that all pairwise state differences of the networked systems converge to zero in an appropriate norm and that the states of these systems satisfy the control objective. The proposed static output feedback controllers thus contain a term that addresses the control objective and a consensus term that ensures synchronization. The synchronization gains of the resulting aggregate systems can be viewed as the strengths of the interconnections among the network nodes. Two different optimization schemes for the non-zero entries of the associated graph Laplacian are proposed. An alternate design proposes the on-line adjustment of the entries of the graph Laplacian matrix via an adaptation involving available output signals of the networked systems. The proposed results are demonstrated by a numerical example for a 1D partial differential equation.