Structural Systems Theory: an overview of the last 15 years

Ramos, Guilherme; Aguiar, A. Pedro; Pequito, Sergio

doi:10.48550/arxiv.2008.11223

Cited by 4 publications

(6 citation statements)

References 236 publications

(295 reference statements)

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“…A survey of research on structural systems theory was recently presented in [13]. We summarize contributions on this topic relevant to our problem in the rest of this section.…”

Section: Related Workmentioning

confidence: 99%

Resilience to Denial-of-Service and Integrity Attacks: A Structured Systems Approach

Ramasubramanian¹,

Rajan²,

Chandra³

et al. 2021

Preprint

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The resilience of cyberphysical systems to denial-of-service (DoS) and integrity attacks is studied in this paper. The cyberphysical system is modeled as a linear structured system, and its resilience to an attack is interpreted in a graph theoretical framework. The structural resilience of the system is characterized in terms of unmatched vertices in maximum matchings of the bipartite graph and connected components of directed graph representations of the system under attack. We first present conditions for the system to be resilient to DoS attacks when an adversary may block access or turn off certain inputs to the system. We extend this analysis to characterize resilience of the system when an adversary might additionally have the ability to affect the implementation of state-feedback control strategies. This is termed an integrity attack. We establish conditions under which a system that is structurally resilient to a DoS attack will also be resilient to a certain class of integrity attacks. Finally, we formulate an extension to the case of switched linear systems, and derive conditions for such systems to be structurally resilient to a DoS attack.

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“…A survey of research on structural systems theory was recently presented in [13]. We summarize contributions on this topic relevant to our problem in the rest of this section.…”

Section: Related Workmentioning

confidence: 99%

Resilience to Denial-of-Service and Integrity Attacks: A Structured Systems Approach

Ramasubramanian¹,

Rajan²,

Chandra³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Due to uncertainty in the system's parameters, we consider a structural systems framework [22]. We introduce the following definition for a structural matrix.…”

Section: A1mentioning

confidence: 99%

“…Moreover, if the parameters are known, the study of controllability and/or observability properties leads to NP-hard problems [25]. Hence, we assume that only the structure of the system is known meaning that a system parameter is either zero or could take on any real scalar value [22]. In this context, we can rely on the notion of structural state and input observability that yields state and input observability for almost all system parameterizations.…”

Section: Introductionmentioning

confidence: 99%

Minimum Structural Sensor Placement for Switched Linear Time-Invariant Systems and Unknown Inputs

Reed¹,

Ramos²,

Bogdan³

et al. 2021

Preprint

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In this paper, we study the structural state and input observability of continuous-time switched linear timeinvariant systems and unknown inputs. First, we provide necessary and sufficient conditions for their structural state and input observability that can be efficiently verified in O((m(n + p)) 2 ), where n is the number of state variables, p is the number of unknown inputs, and m is the number of modes. Moreover, we address the minimum sensor placement problem for these systems by adopting a feed-forward analysis and by providing an algorithm with a computational complexity of O((m(n + p) + α) 2.373 ), where α is the number of target strongly connected components of the system's digraph representation. Lastly, we explore different assumptions on both the system and unknown inputs (latent space) dynamics that add more structure to the problem, and thereby, enable us to render algorithms with lower computational complexity, which are suitable for implementation in large-scale systems.

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“…Notwithstanding, in the context of MADS, we have the freedom of selecting the dynamics weights that would account for the communication protocol between the agents. We propose to leverage structural systems theory, that enables a parametric (i.e., a structure-based) approach to the minimum jointly input and output selection problem [16]. Structural counterparts of controllability and observability hold for almost all parametric choices in infinite fields.…”

Section: Introductionmentioning

confidence: 99%

“…Structural counterparts of controllability and observability hold for almost all parametric choices in infinite fields. Furthermore, they leverage graph-theoretical characterizations in the context of efficient minimum actuator/sensor placement [17,18,16].…”

Section: Introductionmentioning

confidence: 99%

Minimum jointly structural input and output selection for strongly connected networks

Ramos¹,

Aguiar²,

Pequito³

2021

Preprint

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In this paper, given a linear time-invariant strongly connected network, we study the problem of determining the minimum number of state variables that need to be simultaneously actuated and measured to ensure structural controllability and observability, respectively. This problem is fundamental in the design of multi-agent systems, where there are economic constraints in the decision of which agents to equip with a more costly on-board system that will allow the agent to have both actuation and sensing capabilities. Despite the combinatorial nature of this problem, we present a solution that couples the design of both structural controllability and structural observability counterparts to address it with polynomial-time complexity.

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Structural Systems Theory: an overview of the last 15 years

Cited by 4 publications

References 236 publications

Resilience to Denial-of-Service and Integrity Attacks: A Structured Systems Approach

Resilience to Denial-of-Service and Integrity Attacks: A Structured Systems Approach

Minimum Structural Sensor Placement for Switched Linear Time-Invariant Systems and Unknown Inputs

Minimum jointly structural input and output selection for strongly connected networks

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