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— We consider the design of optimal static feedback gains for interconnected systems subject to architectural constraints on the distributed controller. These constraints are in the form of sparsity requirements for the feedback matrix, which means that each controller has access to information from only a limited number of subsystems. We derive necessary(More)
We consider the problem of identifying optimal sparse graph representations of dense consensus networks. The performance of the sparse representation is characterized by the global performance measure which quantifies the difference between the output of the sparse graph and the output of the original graph. By minimizing the sum of this performance measure(More)
—We design sparse and block sparse feedback gains that minimize the variance amplification (i.e., the norm) of distributed systems. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsity-promoting penalty functions into the optimal control problem, where the added terms penalize the number of(More)
—We consider the design of optimal localized feedback gains for one-dimensional formations in which vehicles only use information from their immediate neighbors. The control objective is to enhance coherence of the formation by making it behave like a rigid lattice. For the single-integrator model with symmetric gains, we establish convexity, implying that(More)
(3) is satisfied. APPENDIX B PROOF OF THEOREM 2 The proof is similar to that of Theorem 1. Let a, b, , and be as defined in Appendix A. Then, due to (8), (18), (4), and Lemma 1, we have ^ xi(k) 2 [a; b] 8k 2 8i 2 V and x 3 2 [a; b]. From Lemma 3, lim k!1 V (x(k)) = c for some c 0. To show that c = 0, assume to the contrary that c > 0 and let be as defined(More)
— We examine the leader selection problem in multi-agent dynamical networks where leaders, in addition to relative information from their neighbors, also have access to their own states. We are interested in selecting an a priori specified number of agents as leaders in order to minimize the total variance of the stochastically forced network. Combinatorial(More)
—We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networks. For networks with leaders subject to noise, we show that the(More)
— 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,(More)
We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. Synchronization is achieved when all oscillator voltages reach consensus, and performance is quantified by the mean-square deviation from the consensus value. We formulate optimization problems that address the trade-off between synchronization(More)