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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 Boolean constraints (which indicate whether a...
We study the performance of externally forced leader-follower networks in directed trees and lattices. By exploiting the lower triangular structure of Laplacian matrices of both classes of graphs, we derive explicit formulae for the transfer function from disturbances to the states of the nodes. For directed trees, we show that the worst-case componentwise amplification of disturbances is achieved...
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...
The paper deals with a state observer design for linear systems with disturbances that lie in the control space. We propose a pseudo output, Σ(t), to be included in the observer. It is found that this pseudo output can be related to the measurable output, y(t), by a dynamic mapping which is invariant of the disturbances. Using the inverse method, Σ(t) can be retrieved by y(t) such that the inaccessible...
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