Actuator Placement Under Structural Controllability Using Forward and Reverse Greedy Algorithms

Guo, Baoqiao; Karaca, Orçun; Summers, Tyler H.; Kamgarpour, Maryam

doi:10.1109/tac.2020.3044284

Cited by 18 publications

(18 citation statements)

References 38 publications

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“…Supposing that A − Â ≤ ε and B − B ≤ ε with ε ∈ R >0 , in this subsection we provide an upper bound on Ĵt (S) − J t (S), where J t (S) and Ĵt (S) are defined in Eqs. ( 12) and (18), respectively. We begin with the following result; the proof is included in Appendix A. k be the state corresponding to the certainty equivalence control u…”

Section: Perturbation Bound On Costmentioning

confidence: 99%

“…Due to its combinatorial nature, the problem has been shown to be NP-hard in general (e.g., [38]). Therefore, much work in the literature provides approximation algorithms to solve the problem with performance guarantees (e.g., [28,34,18]), often leveraging results from combinatorial optimization (e.g., [27,7]). However, most of the previous work assumes the system matrices to be known, which is a departure from our work.…”

Section: Related Workmentioning

confidence: 99%

“…Denoting c k = x k Qx k + u k Ru k , where u k = Kk x k , we can rewrite Ĵt (S) defined in Eq. (18) as…”

Section: A4 Proof Of Lemmamentioning

confidence: 99%

See 2 more Smart Citations

Online Actuator Selection and Controller Design for Linear Quadratic Regulation with Unknown System Model

Ye¹,

Ming²,

Liu³

et al. 2022

Preprint

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We study the simultaneous actuator selection and controller design problem for linear quadratic regulation over a finite horizon, when the system matrices are unknown a priori. We propose an online actuator selection algorithm to solve the problem which specifies both a set of actuators to be utilized and the control policy corresponding to the set of selected actuators. Specifically, our algorithm is a model based learning algorithm which maintains an estimate of the system matrices using the system trajectories. The algorithm then leverages an algorithm for the multiarmed bandit problem to determine the set of actuators under an actuator selection budget constraint and also identifies the corresponding control policy that minimizes a quadratic cost based on the estimated system matrices. We show that the proposed online actuator selection algorithm yields a sublinear regret.

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Section: Perturbation Bound On Costmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Online Actuator Selection and Controller Design for Linear Quadratic Regulation with Unknown System Model

Ye¹,

Ming²,

Liu³

et al. 2022

Preprint

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show abstract

“…The size of contractions is also a key property, representing the number of possible options for estimation/observability recovery. A large contraction presents more choices of equivalent state measurements to replace the failed/faulty observation, or, for example, to minimize cost [12][13][14]. Also, the number of contractions represents the number of necessary measurement (or sensors) for estimation.…”

Section: Introductionmentioning

confidence: 99%

Analysis Of Contractions In System Graphs: Application To State Estimation

Doostmohammadian

Charalambous

Shafie‐khah

et al. 2021

2021 IEEE International Conference on Autonomous Systems (ICAS)

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Observability and estimation are closely tied to the system structure, which can be visualized as a system graph-a graph that captures the inter-dependencies within the state variables. For example, in social system graphs such inter-dependencies represent the social interactions of different individuals. It was recently shown that contractions, a key concept from graph theory, in the system graph are critical to system observability, as (at least) one state measurement in every contraction is necessary for observability. Thus, the size and number of contractions are critical in recovering for loss of observability. In this paper, the correlation between the average-size/number of contractions and the global clustering coefficient (GCC) of the system graph is studied. Our empirical results show that estimating systems with high GCC requires fewer measurements, and in case of measurement failure, there are fewer possible options to find substitute measurement that recovers the system's observability. This is significant as by tuning the GCC, we can improve the observability properties of large-scale engineered networks, such as social networks and smart grid.

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“…Since some of these metrics are neither submodular nor supermodular [6], it is in general NP-hard to find the optimal set of actuators positions [7]. 1 The sets minimizing these aforementioned metrics are not guaranteed to make the resulting system controllable, considering that either the metrics are not related to controllability objective at all, or even when they are related, they involve some approximation techniques [12,13]. In view of this issue, structurally controllable systems constitute a desirable class.…”

Section: Introductionmentioning

confidence: 99%

Actuator Placement for Structural Controllability beyond Strong Connectivity and towards Robustness

Guo¹,

Karaca²,

Azhdari³

et al. 2021

Preprint

Self Cite

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Actuator placement is a fundamental problem in control design for large-scale networks. In this paper, we study the problem of finding a set of actuator positions by minimizing a given metric, while satisfying a structural controllability requirement and a constraint on the number of actuators. We first extend the classical forward greedy algorithm for applications to graphs that are not necessarily strongly connected. We then improve this greedy algorithm by extending its horizon. This is done by evaluating the actuator position set expansions at the further steps of the classical greedy algorithm. We prove that this new method attains a better performance, when this evaluation considers the final actuator position set. Moreover, we study the problem of minimal backup placements. The goal is to ensure that the system stays structurally controllable even when any of the selected actuators goes offline, with minimum number of backup actuators. We show that this problem is equivalent to the well-studied NP-hard hitting set problem. Our results are verified by a numerical case study.

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Actuator Placement Under Structural Controllability Using Forward and Reverse Greedy Algorithms

Cited by 18 publications

References 38 publications

Online Actuator Selection and Controller Design for Linear Quadratic Regulation with Unknown System Model

Online Actuator Selection and Controller Design for Linear Quadratic Regulation with Unknown System Model

Analysis Of Contractions In System Graphs: Application To State Estimation

Actuator Placement for Structural Controllability beyond Strong Connectivity and towards Robustness

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