New Zeroing Neural Network Models for Solving Nonstationary Sylvester Equation With Verifications on Mobile Manipulators

Yan, Xiaogang; Liu, Mei; Jin, Long; Li, Shuai; Hu, Bin; Zhang, Xin; Huang, Zhiguan

doi:10.1109/tii.2019.2899428

Cited by 50 publications

(14 citation statements)

References 59 publications

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“…The zeroing dynamics (also known as Zhang dynamics, ZD) method was proposed in 2008, and is based on the error-feedback information [24][25][26]. The ZD method can not only solve the time-varying problems excellently, but also guarantee the exponential convergent performance of time-varying solutions.…”

Section: Introductionmentioning

confidence: 99%

“…The ZD method can not only solve the time-varying problems excellently, but also guarantee the exponential convergent performance of time-varying solutions. Thus, the ZD method has been extensively used in recent years, such as time-varying reciprocal solving [24], time-varying equations solving [25][26][27], Lyapunov equation solving [28,29], and time-varying nonlinear optimization problem [30]. Besides, the schemes designed by the ZD method have also been adopted for many applications, including redundant robot manipulators [30][31][32] and agitator tank [33].…”

Section: Introductionmentioning

confidence: 99%

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Output optimization of scalar and 2‐dimension time‐varying nonlinear systems using zeroing dynamics

Zhang

Shi

Yang

et al. 2020

Asian Journal of Control

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The optimal control of time-varying nonlinear systems is an important research topic and faces many difficulties and challenges, but also has substantial benefits. In this paper, the output optimization of scalar time-varying nonlinear (STVN) system and 2-dimension time-varying nonlinear (2DTVN) system is considered. The zeroing dynamics (ZD) method, which can solve the time-varying problems flexibly and effectively, has been extensively used in recent years. By introducing the ZD method, the time-varying optimal system state is attained, and the controller with the optimal output is designed. Meanwhile, the direct dynamics (DD) method is presented to further illustrate the superiority of the ZD method. Theoretical analyses prove that the ZD method has a faster convergence rate (that is, exponential convergence). In addition, the effectiveness and feasibility of the ZD method for solving the output optimization of STVN and 2DTVN systems are verified by numerical experiments, and further substantiated via output optimization of a two-wheeled mobile robot.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Output optimization of scalar and 2‐dimension time‐varying nonlinear systems using zeroing dynamics

Zhang

Shi

Yang

et al. 2020

Asian Journal of Control

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“…However, on the one hand, lots of methods are essentially designed for solving time-invariant (or say, static) Sylvester matrix equation rather than time-variant Sylvester matrix equation. In this sense, these methods do not possess enough efficiency for handing nonstationary cases due to the lack of adaption to the time-variant parameters [10]. On the other hand, few researches on investigating the discrete-time Sylvester matrix equation compared with the continuous-time one [9,11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Proposing, developing and verification of a novel discrete-time zeroing neural network for solving future augmented Sylvester matrix equation

Shi

Jin

et al. 2020

Journal of the Franklin Institute

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This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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“…Many practical applications in different fields such as industrial manufacture [5], military organizations [6], and public service communities [7] can be ascribed to the motion control of mobile robots. In the recent years, the motion control of mobile robots has been a heated topic for robotic research [8][9][10][11][12][13]. For examples, Yan et al [11] introduced several modified zeroing neural network models for the motion control of mobile robots by considering the non-convex activation functions as well as accelerating the convergence process with finite-time property.…”

Section: Introductionmentioning

confidence: 99%

“…In the recent years, the motion control of mobile robots has been a heated topic for robotic research [8][9][10][11][12][13]. For examples, Yan et al [11] introduced several modified zeroing neural network models for the motion control of mobile robots by considering the non-convex activation functions as well as accelerating the convergence process with finite-time property. In addition, Kapitanyuk et al [13] developed a new scheme for the path-tracking control of nonholonomic mobile robots on the basis of the guiding vector field strategy.…”

Section: Introductionmentioning

confidence: 99%

A recurrent neural network applied to optimal motion control of mobile robots with physical constraints

Chen

Liao

2019

Applied Soft Computing

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Conventional solutions for the motion control of mobile robots in the unified framework of recurrent neural networks (RNNs) are difficult to consider both criteria optimization and physical constraints. To overcome this limitation, this paper proposes a novel inequality and equality constrained optimization RNN (IECORNN) to handle the motion control of mobile robots. Firstly, the real-time motion control problem with both criteria optimization and physical constraints is skillfully converted to a real-time equality system by leveraging the Lagrange multiplier rule. Then, the detailed design process for the proposed IECORNN is presented. Afterward, theoretical analyses on the motion control problem conversion equivalence, global stability, and exponential convergence property are rigorously provided. Finally, numerical experiment verifications and extensive comparisons based on the mobile robot for two different path-tracking applications sufficiently demonstrate the effectiveness and superiority of the proposed IECORNN for the real-time motion control of mobile robots with both criteria optimization and physical constraints.

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New Zeroing Neural Network Models for Solving Nonstationary Sylvester Equation With Verifications on Mobile Manipulators

Cited by 50 publications

References 59 publications

Output optimization of scalar and 2‐dimension time‐varying nonlinear systems using zeroing dynamics

Output optimization of scalar and 2‐dimension time‐varying nonlinear systems using zeroing dynamics

Proposing, developing and verification of a novel discrete-time zeroing neural network for solving future augmented Sylvester matrix equation

A recurrent neural network applied to optimal motion control of mobile robots with physical constraints

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