A linear time algorithm to verify strong structural controllability

Weber, Alexander; Reißig, Gunther; Svaricek, Ferdinand

doi:10.1109/cdc.2014.7040261

Cited by 14 publications

(15 citation statements)

References 19 publications

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“…For this specific size, a simpler algorithm has been presented in [12] and refined in [3], which is equivalent to the one in [11] particularized to this case. A clever implementation of the same algorithm, devised by [13], has a complexity which is linear in the number of vertices plus the number of edges; depending on the sparsity level of the system matrices, this is in between linear and quadratic w.r.t. N + P + M .…”

Section: Resultsmentioning

confidence: 99%

Strongly Structural Input and State Observability for Linear Time Invariant Network Systems

Gracy

Garin

Kibangou

2019

2019 18th European Control Conference (ECC)

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This paper considers linear discrete-time network systems affected by unknown inputs, studying whether they are input and state observable (ISO), namely whether both the initial state and the unknown input can be reconstructed from the output measurements. More precisely, the paper studies ISO, where the input reconstruction must happen with at most one time-step delay, and unconstrained ISO, where a larger delay is allowed. The focus is on strongly structured (unconstrained) ISO, wherein the objective is to find conditions such that for all system matrices that share a given zero/nonzero pattern, the resulting system is (unconstrained) ISO. We first provide a graphical characterization for strongly structural unconstrained ISO. Then, we find a sufficient condition and a necessary condition for strongly structural ISO, which are equivalent in the case without direct feedthrough. All conditions are in terms of existence of suitable uniquely restricted matchings in bipartite graphs associated with the system.

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Section: Resultsmentioning

confidence: 99%

Strongly Structural Input and State Observability for Linear Time Invariant Network Systems

Gracy

Garin

Kibangou

2019

2019 18th European Control Conference (ECC)

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“…To check if the system is strong structurally controllable with given inputs, an algorithm based on constrained matchings in bipartite graphs with time complexity O(n 2 ) was given in [3]. In [14], an algorithm with a run time linear in the number of nodes and edges was presented to verify whether a system is strong structurally controllable. The relationship of SSC and zero forcing sets (ZFS) was explored in [15], [16], and it was established that checking if a system is strong structurally controllable with given input nodes is equivalent to checking if the set of input nodes is a ZFS in the underlying network graph.…”

Section: A Related Workmentioning

confidence: 99%

On the Computation of the Distance-based Lower Bound on Strong Structural Controllability in Networks

Shabbir

Abbas

Yazıcıoğlu

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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A network of agents with linear dynamics is strong structurally controllable if agents can be maneuvered from any initial state to any final state independently of the coupling strengths between agents. If a network is not strong structurally controllable with a given set of input nodes (leaders), then the dimension of strong structurally controllable subspace quantifies the extent to which a network can be controlled by the same inputs. Computing this dimension exactly is computationally challenging. In this paper, we study the problem of computing a sharp lower bound on the dimension of strong structurally controllable subspace in networks with Laplacian dynamics. The bound is based on a sequence of vectors containing distances between leaders and the remaining nodes in the underlying network graph. Such vectors are referred to as the distanceto-leader vectors. We provide a polynomial time algorithm to compute a particular sequence of distance-to-leader vectors with a fixed set of leaders, which directly provides a lower bound on the dimension of strong structurally controllable subspace. We also present a linearithmic approximation algorithm to compute such a sequence, which provides near optimal solutions in practice. Using these results, we also explore connections between graph-theoretic properties and length of longest such sequences in path and cycle graphs. Finally, we numerically evaluate and compare our bound with other bounds in the literature on various networks. arXiv:1909.03565v1 [eess.SY]

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“…More recently, building on the works [6,7], a characterization in terms of existence of uniquely restricted matchings of appropriate size on suitably-defined bipartite graphs has been provided in [8], together with a polynomial-time algorithm to test such condition. This approach has been used in further works such as [9,10]. Yet another approach towards studying s-structural controllability is that of zero forcing sets [11,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Strong structural input and state observability of linear time-invariant systems: Graphical conditions and algorithms

Garin

Gracy

Kibangou

2021

European Journal of Control

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The paper studies input and state observability (ISO) of discrete-time linear time-invariant network systems whose dynamics are a↵ected by unknown inputs. More precisely, we aim at reconstructing the initial state and the sequence of unknown inputs from the system outputs, and we will use the term ISO when the input reconstruction is possible with delay one, namely the inputs up to time k 1 and the states up to time k can be obtained from the outputs up to time k, while the term unconstrained ISO will refer to the case where there is some arbitrary delay in the input reconstruction. We focus on the problem of s-structural ISO (resp. s-structural unconstrained ISO) wherein the objective is to find conditions such that for all system matrices that carry the same network structure, the resulting system is ISO (resp. unconstrained ISO). We provide first a graphical characterization for s-structural unconstrained ISO, and subsequently, su cient conditions and necessary conditions for s-structural ISO. For the latter, under the assumption of zero feedthrough, these conditions coincide and characterise ISO. The conditions presented are in terms of existence of suitable uniquely restricted matchings in bipartite graphs associated with the structured system. In order to test these conditions, we present polynomial-time algorithms. Finally, we discuss an equivalent reformulation of the main conditions in terms of coloring algorithms as in the literature of zero forcing sets.

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A linear time algorithm to verify strong structural controllability

Cited by 14 publications

References 19 publications

Strongly Structural Input and State Observability for Linear Time Invariant Network Systems

Strongly Structural Input and State Observability for Linear Time Invariant Network Systems

On the Computation of the Distance-based Lower Bound on Strong Structural Controllability in Networks

Strong structural input and state observability of linear time-invariant systems: Graphical conditions and algorithms

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