The Jordan canonical form for a class of weighted directed graphs

Nina, Hans; Soto, Ricardo L.; Cardoso, Domingos M.

doi:10.1016/j.laa.2012.07.038

Cited by 5 publications

(3 citation statements)

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“…where A = −39.5257, B = 1, C = 60.4743 and D = 0. There is a number of methods to derive a state-space from a given transfer function and the Jordan canonical form used in (2) is only one of them [9].…”

Section: The Aim and Objectives Of The Studymentioning

confidence: 99%

Realisation of MPC Algorithm for Quanser Qube-Servo

Assanova,

Khaimuldin,

Khaimuldin

et al. 2023

sjaitu

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This paper offers an in-depth look into the design and implementation of a Model Predictive Control (MPC) algorithm for the QUANSER QUBE-SERVO system. The QUBE-SERVO is a sophisticated laboratory experimental setup consisting of a servo motor, an encoder, and a rotary module. This combination provides a robust platform for investigating and testing various control strategies. In particular, the central focus of this study is the usage of the MPC algorithm for controlling the position of the QUBE-SERVO’s rotary disc load module. The MPC algorithm plays a pivotal role in this application by predicting the future behaviors of the system, and controlling the system by minimizing an objective function over a defined finite horizon. This makes it a versatile and effective tool for controlling complex systems. One of the key challenges in practical control applications is maintaining system stability in the presence of disturbances and uncertainties. To this end, we propose a MPC algorithm designed specifically to stabilize the QUBE-SERVO under such conditions. The functionality of this algorithm is not limited to the QUBE-SERVO system alone, and can be extended to other control systems exhibiting similar characteristics. The effectiveness of the proposed MPC algorithm is rigorously tested through simulation studies. These studies involve subjecting the QUBE-SERVO to various reference signals and disturbances. The results of the simulations provide strong evidence of the algorithm’s capability to effectively track reference signals, while also rejecting disturbances and uncertainties, thereby corroborating its efficacy for the QUBE-SERVO application. Moreover, the original MPC algorithm was enhanced to improve its performance for trajectory tracking tasks. We also discuss the integration of the MPC algorithm within the MatLAB and LabVIEW programming environments, which served as the base platforms for designing and running the simulations in this project. This paper, therefore, presents a comprehensive and practical approach for the successful implementation of the MPC algorithm in the QUANSER QUBE-SERVO system, and demonstrates its potential for wider application in similar control systems.

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Section: The Aim and Objectives Of The Studymentioning

confidence: 99%

Realisation of MPC Algorithm for Quanser Qube-Servo

Assanova,

Khaimuldin,

Khaimuldin

et al. 2023

sjaitu

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“…enable the GFT to be equivalent over multiple graph structures. It may be sufficient to find these classes by traversing the graph once (with total time complexity 𝑂(|𝑉 | + |𝐸|)) and then determining the Jordan normal form of the underlying graph because of the acyclic and cyclic structures within the graph; see [24], [25] and more details in Section IV.…”

Section: Frequency Ordering Of Spectral Componentsmentioning

confidence: 99%

“…Certain types of matrices have Jordan forms that can be deduced from their graph structure. For example, [24] and [25] relate the Jordan blocks of certain adjacency matrices to a decomposition of their graph structures into unions of cycles and chains. Applications where such graphs are in use would allow a practitioner to determine the Jordan equivalence classes (assuming the eigenvalues can be computed) and potentially choose a different matrix in the class for which the GFT can be computed more easily.…”

mentioning

confidence: 99%

Spectral Projector-Based Graph Fourier Transforms

Deri

Moura

2017

IEEE J. Sel. Top. Signal Process.

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Abstract-The paper presents the graph Fourier transform (GFT) of a signal in terms of its spectral decomposition over the Jordan subspaces of the graph adjacency matrix . This representation is unique and coordinate free, and it leads to unambiguous definition of the spectral components ("harmonics") of a graph signal. This is particularly meaningful when has repeated eigenvalues, and it is very useful when is defective or not diagonalizable (as it may be the case with directed graphs). Many real world large sparse graphs have defective adjacency matrices. We present properties of the GFT and show it to satisfy a generalized Parseval inequality and to admit a total variation ordering of the spectral components. We express the GFT in terms of spectral projectors and present an illustrative example for a real world large urban traffic dataset.

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