A Framework for Structural Input/Output and Control Configuration Selection in Large-Scale Systems

Pequito, Sérgio; Kar, Soummya; Aguiar, A. Pedro

doi:10.1109/tac.2015.2437525

Cited by 226 publications

(293 citation statements)

References 22 publications

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“…Yet, if we need to guarantee only structural controllability, MCP1 can be easily solved (Pequito et al, 2013(Pequito et al, , 2016. For a directed network G with LTI dynamics the minimum number of dedicated inputs (or actuators), N da , required to assure structural controllability, is…”

Section: E Minimal Controllability Problemsmentioning

confidence: 99%

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Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

543

349

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A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: it requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

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Section: E Minimal Controllability Problemsmentioning

confidence: 99%

“…The maximum assignability index of B(G) is the maximum number of top assignable SCCs that a maximum matching M * may lead to. The minimum set of actuators can be found with polynomial time complexity (Pequito et al, 2013(Pequito et al, , 2016. Consider, for example, the network shown in Fig.…”

Section: E Minimal Controllability Problemsmentioning

confidence: 99%

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

543

349

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“…, n} be the set of indices i of iterations of OKS such that after the i-th iteration the minimum degree on the right side of the network is larger than one. Since the set {0 < t < T : m(x(t)) > 1} has zero Lebesgue measure by (27) Lebesgue measure of the set {0 < t < T : m(X (n) (t)) > 1} goes to 0 as n grows. Because the Lebesgue measure of the set {0 < t < T : m(X (n) (t)) > 1} is i∈J (n) τ i+1 we have lim n→∞ i∈J (n) τ i+1 = 0 but by the Law of Large Numbers lim…”

Section: Properties Of the Asymptotic Initial Value Problemsmentioning

confidence: 99%

Optimality of Fast-Matching Algorithms for Random Networks With Applications to Structural Controllability

Faradonbeh¹,

Tewari

Michailidis

2017

IEEE Trans. Control Netw. Syst.

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Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There are many notions of controllability, one of them being structural controllability, which is intimately connected to finding maximum matchings on the underlying network topology. In this work, we study fast, scalable algorithms for finding maximum matchings for a large class of random networks. First, we illustrate that degree distribution random networks are realistic models for real networks in terms of structural controllability. Subsequently, we analyze a popular, fast and practical heuristic due to Karp and Sipser as well as a simplification of it. For both heuristics, we establish asymptotic optimality and provide results concerning the asymptotic size of maximum matchings for an extensive class of random networks.

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“…B(S 1 , S 2 , E S1,S2 ) and a maximum matching M * ) correspond to those vertices in S 1 that do not belong to a matched edge in M * . The following results will be required [11]. Lemma 1 ( [11]): Given D(Ā) = (X , E X ,X ), a bipartite graph B(X , X , E X ,X ) has a perfect match if and only if D(Ā) is spanned by a disjoint union of cycles.…”

Section: Preliminaries and Terminologymentioning

confidence: 99%

“…Remark 11]): Let D(Ā) = (X , E X ,X ) denote the system digraph and the state bipartite graph B ≡ B(X , X , E X ,X ), i.e., the bipartite representation of D(Ā). Let S y ⊂ X , then the following statements are equivalent:…”

Section: Preliminaries and Terminologymentioning

confidence: 99%

Optimal design of observable multi-agent networks: A structural system approach

Pequito

Rego

Kar

et al. 2014

2014 European Control Conference (ECC)

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Abstract-This paper introduces a method to design observable directed multi-agent networks, that are: 1) either minimal with respect to a communications-related cost function, or 2) idem, under possible failure of direct communication between two agents. An observable multi-agent network is characterized by agents that update their states using a neighboring rule based on directed communication graph topology in order to share information about their states; furthermore, each agent can infer the initial information shared by all the agents. Sufficient conditions to ensure that 1) is satisfied are obtained by reducing the original problem to the travelling salesman problem (TSP). For the case described in 2), sufficient conditions for the existence of a minimal network are shown to be equivalent to the existence of two disjoint solutions to the TSP. The results obtained are illustrated with an example from the area of cooperative path following of multiple networked vehicles by resorting to an approximate solution to the TSP.

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A Framework for Structural Input/Output and Control Configuration Selection in Large-Scale Systems

Cited by 226 publications

References 22 publications

Control principles of complex systems

Control principles of complex systems

Optimality of Fast-Matching Algorithms for Random Networks With Applications to Structural Controllability

Optimal design of observable multi-agent networks: A structural system approach

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