A nonlinear robust PI controller for an uncertain system

Aguilar-Ibáñez, Carlos; Mendoza-Mendoza, Julio Alberto; Suárez-Castañón, Miguel S.; Dávila, Jorge

doi:10.1080/00207179.2013.868606

Cited by 9 publications

(3 citation statements)

References 34 publications

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“…, then it has an eigenvalue (l*) that is positive and greater than or equal to all other eigenvalues [37][38][39][40], that is…”

Section: Methods Of [28]mentioning

confidence: 99%

“…Equation (7) can be rewritten using the normalisation factor a ij as

γ_{j} = \frac{p_{j}}{\sum_{i = 1, i \neq j}^{N} p_{i} a_{i j}}

where

a_{i j} = ({, \begin{matrix} 1em4pt \\ \frac{g_{_{i j}}^{normalF}}{g_{_{j j}}^{normalF}}, & if i \neq j \\ 1, & if i = j \end{matrix})

All normalised link gains construct the normalised gain matrix

A = false[a_{i j} false]

. According to the Perron–Frobenius theorem [36], if A is an N × N normalised gain matrix, which is irreducible and non‐negative with eigenvalues

{\{λ_{i}\}}_{i = 1}^{N}

, then it has an eigenvalue ( λ *) that is positive and greater than or equal to all other eigenvalues [37–40], that is

λ^{*} = truemax {\{|λ_{i}|\}}_{i = 1}^{N}

Therefore, there is a positive eigenvector p * corresponding to the largest eigenvalue λ* that satisfies the following equation:

λ^{*} p^{*} = A p^{}

…”

Section: Introductionmentioning

confidence: 99%

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Femtocell base station clustering and logistic smooth transition autoregressive‐based predicted signal‐to‐interference‐plus‐noise ratio for performance improvement of two‐tier macro/femtocell networks

Lotfollahzadeh¹,

Kabiri²,

Kalbkhani³

et al. 2016

IET signal process.

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The aim of this study is to improve the performance of two-tier macro/femtocell networks using a power control approach. In wireless networks, power control plays an important role in improving a number of performance parameters such as co-channel interference and outage probability reduction, throughput increasing, and power saving. This study explores the evolution of centralised power control algorithm based on femtocell base station (FBS) clustering and predicted signal-to-interference-plus-noise ratio (SINR) of users. To reduce the computational complexity of centralised algorithm, dense deployed femtocells are considered in different clusters. In this case, femtocells inside one cluster make considerable interference to each other, while the interferences from femtocells of other clusters are negligible. Moreover, because of the non-linearity of SINR samples, non-linear logistic smooth transition autoregressive (LSTAR) model is used to model the SINR data, and then the next SINR samples are predicted from the previous samples. A c c o r d i n gt ot h ec l u s t e r e dF B S sa n dp r e d i c t e dS I N R ,t h e proposed power control scheme is applied to femtocell network in the downlink. The results demonstrate that the introduced method improves the outage probability and throughput and outperforms previous methods significantly.

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“…, then it has an eigenvalue (l*) that is positive and greater than or equal to all other eigenvalues [37][38][39][40], that is…”

Section: Methods Of [28]mentioning

confidence: 99%

“…Equation (7) can be rewritten using the normalisation factor a ij as

γ_{j} = \frac{p_{j}}{\sum_{i = 1, i \neq j}^{N} p_{i} a_{i j}}

where

a_{i j} = ({, \begin{matrix} 1em4pt \\ \frac{g_{_{i j}}^{normalF}}{g_{_{j j}}^{normalF}}, & if i \neq j \\ 1, & if i = j \end{matrix})

All normalised link gains construct the normalised gain matrix

A = false[a_{i j} false]

. According to the Perron–Frobenius theorem [36], if A is an N × N normalised gain matrix, which is irreducible and non‐negative with eigenvalues

{\{λ_{i}\}}_{i = 1}^{N}

, then it has an eigenvalue ( λ *) that is positive and greater than or equal to all other eigenvalues [37–40], that is

λ^{*} = truemax {\{|λ_{i}|\}}_{i = 1}^{N}

Therefore, there is a positive eigenvector p * corresponding to the largest eigenvalue λ* that satisfies the following equation:

λ^{*} p^{*} = A p^{}

…”

Section: Introductionmentioning

confidence: 99%

Femtocell base station clustering and logistic smooth transition autoregressive‐based predicted signal‐to‐interference‐plus‐noise ratio for performance improvement of two‐tier macro/femtocell networks

Lotfollahzadeh¹,

Kabiri²,

Kalbkhani³

et al. 2016

IET signal process.

View full text Add to dashboard Cite

show abstract

“…Since the VSC controller (18) contains the sign function, direct application of such control signals to the robotic system (1) may result in chattering caused by the signal discontinuity. To overcome this problem, the control law is smoothed out within a thin boundary layer [18,28] by replacing the sign function by a saturation function defined as sat (…”

Section: Remarkmentioning

confidence: 99%

Adaptive Robust Quadratic Stabilization Tracking Control for Robotic System with Uncertainties and External Disturbances

Peng

Liu

2014

Journal of Control Science and Engineering

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An adaptive robust quadratic stabilization tracking controller with hybrid scheme is proposed for robotic system with uncertainties and external disturbances. The hybrid scheme combines computed torque controller (CTC) with an adaptive robust compensator, in which variable structure control (VSC) andH∞optimal control approaches are adopted. The uncertain robot manipulator is mainly controlled by CTC, the VSC is used to eliminate the effect of the uncertainties and ensure global stability, andH∞approach is designed to achieve a certain tracking performance of closed-loop system. A quadratic stability approach, which allows separate treatment of parametric uncertainties, is used to reduce the conservatism of the conventional robust control approach. It can be also guaranteed that all signals in closed-loop system are bounded. The validity of the proposed control scheme is shown by computer simulation of a two-link robotic manipulator.

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