On the metric determination of linear dependence graph

Salman, Muhammad; Rasheed, Nimra; Rehman, Masood Ur; Alsaedi, Ahmed

doi:10.1002/oca.2883

Optim Control Appl Methods

2022

DOI: 10.1002/oca.2883

|View full text |Cite

On the metric determination of linear dependence graph

Muhammad Salman

Nimra Rasheed

Masood Ur Rehman

et al.

Abstract: The metric on a connected graph G is a mapping which assigns to each pair (u, v) of vertices in G the length of a shortest path between u and v. In this article, we consider the linear dependence graph associated with a finite dimensional vector space and determine its metric properties, namely, the center, the periphery, metric-degree sequence, metric-degree polynomial, metric dimension, connected metric dimension, local metric dimension, strong metric dimension, and the metric polynomial.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

2023

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(4 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The seventh group of papers 31‐36 focuses on machine learning, data mining, and practical applications in automation. The performance of a Takagi–Sugeno fuzzy‐model‐based observer is enhanced by proposing a featured multi‐instant united switch‐type observer 31 .…”

mentioning

confidence: 99%

“…A novel collaborative diagnosis method is presented by combining variational modal decomposition and stochastic configuration network for incipient faults of rolling bearing 35 . The linear dependence graph associated with a finite‐dimensional vector space is studied 36 …”

mentioning

confidence: 99%

“…29 An algorithm called the kernel entropy regression is proposed to enhance the interpretability between the fault and the key performance indicator. 30 The seventh group of papers [31][32][33][34][35][36] focuses on machine learning, data mining, and practical applications in automation. The performance of a Takagi-Sugeno fuzzy-model-based observer is enhanced by proposing a featured multi-instant united switch-type observer.…”

mentioning

confidence: 99%

“…35 The linear dependence graph associated with a finite-dimensional vector space is studied. 36 In summary, this special issue provides an opportunity to review the most recent developments in data-based learning control for optimization of nonlinear systems, by considering theory, algorithms, and applications.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Data‐based learning control for optimization of nonlinear systems

Wei

Song

Zhang

et al. 2023

Optim Control Appl Methods

View full text Add to dashboard Cite

With the development of science and technology, practical systems such as the power systems, traffic systems, robot manipulator systems, etc., have become more complex. Therefore, it is difficult to build practical systems by accurate models. Under the lack of accurate process models, using system data to improve system performance and learn optimal decisions becomes very important. Through the recent years, data-based learning control theories and technologies have widely been investigated, including adaptive dynamic programming, reinforcement learning, iterative learning control, and so on. Data-based methods require the system data instead of the accurate knowledge of system dynamics that can be considered as model-free learning control methods. The data-based methods are effective solutions for the optimal control of nonlinear systems, which motivate this special issue.This special issue aims to collect and present original research dealing with data-based learning and their applications for optimization and control problems. The first group of papers [1][2][3][4][5][6][7] focuses on data-based control theory, approaches, and applications. A fuzzy model predictive control approach is proposed for stick-slip type piezoelectric actuator to realize the precise control of the end effector. 1 A systematic online adaptive dynamic programming control framework is proposed for smart buildings control to ensure hard constraints to be satisfied. 2 A multi-verse optimizer tuned PI-type active disturbance rejection generalized predictive control method is described for the motion control problems of ships. 3 The sufficient optimality conditions for the optimal controls are established under some convexity assumptions. 4 A receding-horizon reinforcement learning algorithm is proposed for near-optimal control of continuous-time systems under control constraints. 5 In order to solve the interference compensation control problem of a class of nonlinear systems, a method based on memory data is introduced to suppress interference greatly. 6 A new controller design method is proposed for the trajectory tracking problem of robots with imprecise dynamic properties and interference. 7 The second group of papers 8-12 considers iterative learning identification and iterative learning control. An iterative learning control approach is proposed for linear parabolic distributed parameter systems with multiple actuators and multiple sensors. 8 The quantized data-based iterative learning tracking control problem is studied for nonlinear networked control systems with signals quantization and denial-of-service attacks. 9 The output tracking problem is considered for a class of nonlinear parabolic distributed parameter systems with moving boundaries. 10 A just-in-time learning based dual heuristic programming algorithm is proposed to optimize the control performance of autonomous wheeled mobile robots under faults or disturbances. 11 A novel optimal constraint-following controller is proposed for uncertain mechanical systems. 12 The third...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Data‐based learning control for optimization of nonlinear systems

Wei

Song

Zhang

et al. 2023

Optim Control Appl Methods

View full text Add to dashboard Cite

show abstract

Metric Properties of Non-Commuting Graph Associated to Two Groups

Mukhtar

Salman

Maden

et al. 2022

Int. J. Found. Comput. Sci.

View full text Add to dashboard Cite

The non-commuting graph associated to a group has non-central elements of the graph as vertices and two elements [Formula: see text] and [Formula: see text] do not form an edge if and only if [Formula: see text]. In this paper, we consider non-commuting graphs associated to dihedral and semidihedral groups. We investigate their metric properties such as center, periphery, eccentric graph, closure and interior. We also perform various types of metric identifications on these graphs. Moreover, we generate metric and metric-degree polynomials of these graphs.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

On the metric determination of linear dependence graph

Cited by 2 publications

References 40 publications

Data‐based learning control for optimization of nonlinear systems

Data‐based learning control for optimization of nonlinear systems

Metric Properties of Non-Commuting Graph Associated to Two Groups

Contact Info

Product

Resources

About