Algorithms for leader selection in large dynamical networks: Noise-free leaders

We consider networks of single-integrator systems, where it is desired to optimally assign a predetermined number of systems to act as leaders. Performance is measured in terms of the ℋ₂ norm of the overall network, and the leaders are assumed to always follow their desired state trajectories. We demonstrate that, after applying a sequence of relaxations, the problem can be formulated as a semidefinite program and thus solved efficiently. We compare the results of our algorithms against others reported in the literature. Finally, we interpret the leader selection problem in terms of electrical networks and Kron reduction theory.