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14
On Submodularity and Controllability in Complex Dynamical Networks
, 2014
"... Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem is sensor and actuator placement: choose a subset from a fini ..."
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Cited by 6 (1 self)
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Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem is sensor and actuator placement: choose a subset from a finite set of possible placements to optimize some realvalued controllability and observability metrics of the network. Surprisingly little is known about the structure of such combinatorial optimization problems. In this paper, we show that several important classes of metrics based on the controllability and observability Gramians have a strong structural property that allows for either efficient global optimization or an approximation guarantee by using a simple greedy heuristic for their maximization. In particular, the mapping from possible placements to several scalar functions of the associated Gramian is either a modular or submodular set function. The results are illustrated on randomly generated systems and on a problem of power electronic actuator placement in a model of the European power grid.
Controllability and fraction of leaders in infinite networks
 in Decision and Control (CDC), IEEE 53rd Annual Conference on, 2014
"... Abstract—In this paper, we study controllability of a network of linear singleintegrator agents when the network size goes to infinity. We first investigate the effect of increasing size by injecting an input at every node and requiring that network controllability Gramian remain wellconditioned w ..."
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Abstract—In this paper, we study controllability of a network of linear singleintegrator agents when the network size goes to infinity. We first investigate the effect of increasing size by injecting an input at every node and requiring that network controllability Gramian remain wellconditioned with the increasing dimension. We provide theoretical justification to the intuition that high degree nodes pose a challenge to network controllability. In particular, the controllability Gramian for the networks with bounded maximum degrees is shown to remain wellconditioned even as the network size goes to infinity. In the canonical cases of star, chain and ring networks, we also provide closedform expressions which bound the condition number of the controllability Gramian in terms of the network size. We next consider the effect of the choice and number of leader nodes by actuating only a subset of nodes and considering the
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"... Control of coupled oscillator networks with application to microgrid technologies ..."
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Control of coupled oscillator networks with application to microgrid technologies
Minimum Cost Input/Output Design for LargeScale Linear Structural Systems
, 2015
"... In this paper, we provide optimal solutions to two different (but related) input/output design problems involving largescale linear dynamical systems, where the cost associated to each directly actuated/measured state variable can take different values, but is independent of the labeled input/outpu ..."
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In this paper, we provide optimal solutions to two different (but related) input/output design problems involving largescale linear dynamical systems, where the cost associated to each directly actuated/measured state variable can take different values, but is independent of the labeled input/output variable. Under these conditions, we first aim to determine and characterize the input/output placement that incurs in the minimum cost while ensuring that the resulting placement achieves structural controllability/observability. Further, we address a constrained variant of the above problem, in which we seek to determine the minimum cost placement configuration, among all possible input/output placement configurations that ensures structural controllability/observability, with the lowest number of directly actuated/measured state variables. We show that both problems can be solved efficiently, i.e., using algorithms with polynomial time complexity in the number of the state variables. Finally, we illustrate the obtained results with an example.
1On the Role of Network Centrality in the Controllability of Complex Networks
"... Abstract—In recent years complex networks have gained increasing attention in different fields of science and engineering. The problem of controlling these networks is an interesting and challenging problem to investigate. In this paper we look at the controllability problem focusing on the energy ..."
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Abstract—In recent years complex networks have gained increasing attention in different fields of science and engineering. The problem of controlling these networks is an interesting and challenging problem to investigate. In this paper we look at the controllability problem focusing on the energy needed for the control. Precisely not only we want to analyze whether a network can be controlled, but we also want to establish whether the control can be performed using a limited amount of energy. We restrict our study to irreducible and (marginally) stable networks and we find that the leading right and left eigenvectors of the network matrix play a crucial role in this analysis. Interestingly, our results suggest the existence of a connection between controllability and network centrality, a wellknown concept in network science. In case the network is reversible, the latter connection involves the PageRank, an extensively studied type of centrality measure. Finally, the proposed results are applied to examples concerning random graphs. Index Terms—Complex networks, controllability, network centrality, PageRank. I.