Linear Simultaneous Equations’ Neural Solution and Its Application to Convex Quadratic Programming with Equality-Constraint

Chen, Yuhuan; Chen, Yi; Zhong, Jian

doi:10.1155/2013/695647

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…(20)-(23) by using the abovementioned SPGD method, the energy function ε and the estimated parameters {p j } are corresponding to the minimized performance metric and the increment of control parameter, respectively. Therefore, the metric change δ ε with ε(•) is (24) and…”

Section: Spgd Design Proceduresmentioning

confidence: 99%

“…Recent studies have shown that Zhang dynamics (ZD) is designed and developed for the time-varying problems solving [22]- [24]. By using the combination of ZD and gradientbased dynamics (GD), the authors in [22] have presented a tracking controller in the form ofu (i. e., the time-derivation of control action u) for a class of nth-order nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

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Research on a New Singularity-Free Controller for Uncertain Lorenz System

Chen

2019

IEEE Access

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It is a challenge problem to stably control the well-known Lorenz system with uncertain parameters because of its nonlinearity and singularity. In this paper, by combining Zhang dynamics (ZD) and gradient-algorithm, a novel Zhang-Gradient (ZG) controller is designed and developed for solving the controlling problem of the uncertainty Lorenz system. In order to improve computing efficiency, the stochastic parallel gradient descent algorithm is also introduced to perform an incremental adjustment of the unknown parameters for the uncertain Lorenz system. The presented theoretical analysis in this paper shows that our such presented method could conquer the possible singularity which is a difficult problem in typical backstepping controller design. The computer simulation results exhibit that, the controlled system can be stable globally and the tracking error converges to zero asymptotically, which are further demonstrate the effectiveness and feasibility of our presented ZG controller.

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Section: Spgd Design Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Research on a New Singularity-Free Controller for Uncertain Lorenz System

Chen

2019

IEEE Access

Self Cite

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New Discrete-Time ZNN Models for Least-Squares Solution of Dynamic Linear Equation System With Time-Varying Rank-Deficient Coefficient

Qiu

Zhang

Yang

2018

IEEE Trans. Neural Netw. Learning Syst.

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In this brief, a new one-step-ahead numerical differentiation rule called six-instant -cube finite difference (6I CFD) formula is proposed for the first-order derivative approximation with higher precision than existing finite difference formulas (i.e., Euler and Taylor types). Subsequently, by exploiting the proposed 6I CFD formula to discretize the continuous-time Zhang neural network model, two new-type discrete-time ZNN (DTZNN) models, namely, new-type DTZNNK and DTZNNU models, are designed and generalized to compute the least-squares solution of dynamic linear equation system with time-varying rank-deficient coefficient in real time, which is quite different from the existing ZNN-related studies on solving continuous-time and discrete-time (dynamic or static) linear equation systems in the context of full-rank coefficients. Specifically, the corresponding dynamic normal equation system, of which the solution exactly corresponds to the least-squares solution of dynamic linear equation system, is elegantly introduced to solve such a rank-deficient least-squares problem efficiently and accurately. Theoretical analyses show that the maximal steady-state residual errors of the two new-type DTZNN models have an pattern, where denotes the sampling gap. Comparative numerical experimental results further substantiate the superior computational performance of the new-type DTZNN models to solve the rank-deficient least-squares problem of dynamic linear equation systems.

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Linear Simultaneous Equations’ Neural Solution and Its Application to Convex Quadratic Programming with Equality-Constraint

Cited by 2 publications

References 17 publications

Research on a New Singularity-Free Controller for Uncertain Lorenz System

Research on a New Singularity-Free Controller for Uncertain Lorenz System

New Discrete-Time ZNN Models for Least-Squares Solution of Dynamic Linear Equation System With Time-Varying Rank-Deficient Coefficient

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