Synchronization and consensus controllers for a class of parabolic distributed parameter systems

This work examines the consensus control problem for a class of partial differential equations with a Riesz-spectral state operator. The objective is to design controllers that ensure that the state of each of the N systems agrees with the remaining states and at the same time achieves the control objectives of tracking or regulation. Both the case of full state and partial state availability are considered and in the special case of Riesz-spectral operators, one can obtain an explicit bound on the convergence rate of the pairwise state errors. The results are also extended to the case where the all-to-all connectivity among the N systems assumption is relaxed. Extensive numerical studies provide a further insight on the effects of consensus control.