Continuous and discrete time Zhang dynamics for time-varying 4th root finding

Zhang, Yunong; Xiao, Lin; Ruan, Gongqin; Li, Zhan

doi:10.1007/s11075-010-9410-0

Cited by 24 publications

(3 citation statements)

References 17 publications

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“…This characteristic of ZNN enables it to handle some engineering problems involving time-varying, but there is another point that cannot be ignored in the application process, which is the processing of nonlinear time-varying, that is, discrete time-varying problems. To make ZNN play a role in practical engineering problems and reduce time-varying nonlinearity, discrete-time ZNN (DTZNN), which originates from discretization of continuous-time zeroing neural network (CTZNN), can be thought of as a useful tool for resolving discrete time-varying issues 7 .…”

Section: Introductionmentioning

confidence: 99%

A zeroing neural network for solving discrete time-varying minimization with different adjustable parameter

2023

Seventh International Conference on Mechatronics and Intelligent Robotics (ICMIR 2023)

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It is popular approach to employ zeroing neural networks (ZNN) to handle time-varying problems. However, most of the existing methods have limited flexibility in the discretization process, which seriously affects the final effect of the model. To solve this problem, in this paper, we present a new discrete-time ZNN (DTZNN) for handling discrete time-varying minimization problem. In detail, the new DTZNN is proposed with four-instant general discretization formula, which has a adjustable parameter d . Generally speaking, in the process of discretization, different values of d and time interval can influence the residual error observably. In order to verify the effectiveness of our method, we conduct multiple numerical experiments. The numerical experiment results show that the new DTZNN has effectiveness and superiority for handling discrete time-varying minimization problem.

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Section: Introductionmentioning

confidence: 99%

A zeroing neural network for solving discrete time-varying minimization with different adjustable parameter

2023

Seventh International Conference on Mechatronics and Intelligent Robotics (ICMIR 2023)

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“…Mathematically, the corresponding system control can be transformed into the time-varying problem solving [3,4], e.g., time-varying matrix inversion [5,6] and time-varying optimization [7,8]. Zeroing dynamics (ZD) [9][10][11][12][13][14] is a systematic method to solve these kinds of time-varying problems. For example, in [11], a ZD algorithm was developed for time-varying nonlinear equations solving.…”

Section: Introductionmentioning

confidence: 99%

Relationship between time-instant number and precision of ZeaD formulas with proofs

Yang

Zhang

2021

Numer Algor

Self Cite

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Recently, zeroing dynamics (ZD) method has shown wonderful effect in solving time-varying problems. Generally, the continuous-time ZD model should be discretized as a discrete-time algorithm for numerical computation. A good choice is to apply Zhang et al. discretization (ZeaD) formulas, which are effective timediscretization formulas. Actually, ZeaD formulas can also be applied to obtaining various discrete-time algorithms, not only the ZD algorithms. In the previous work, some piecemeal ZeaD formulas have been proposed and investigated. However, the relationship between the time-instant number and precision of ZeaD formulas is not found, which is emphatically investigated in this paper. Specifically, the ZeaD formulas from two to nine instants are investigated, and the general ZeaD formula groups are studied. Two-instant and three-instant ZeaD formula groups have linear precision at most. Four-instant ZeaD formula group has quadratic precision at most. Five-instant and six-instant ZeaD formula groups have cubic precision at most. Seven-instant and eight-instant ZeaD formula groups have quartic precision at most. Nine-instant ZeaD formula group has quintic precision at most. Theoretical analyses are presented to substantiate the relationship. Moreover, the ZeaD formulas as well as ZD method are applied to solving time-varying quadratic optimization problem, and the numerical results verify the effectiveness of ZeaD formulas.

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“…Y. Zhang, B. Liao, L. Jin et al researched on a series of problems such as time-variant matrix inversion, time-variant polynomial root searching, and time-variant nonlinear optimization. They compared several discretization methods and proved the convergency of discrete recurrent neural network [36][37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Discretized Mid‐Value CLVI‐PDNN Based Redundancy Resolution for Single Leg of Quadruped Robot

Rao

Zhang

et al. 2019

Mathematical Problems in Engineering

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The two most important performance indicators of quadruped robot are load capacity and walking speed, and these performance indicators of the whole robot finally reflect on the joint torques and angular velocities. To satisfy different requirements of walking speed and load capacity when quadruped robots implement different tasks, the joint torques and angular velocities need to be balanced with physical constraints of the joints. A single leg with redundant DOF (degree of freedom) could optimize the distribution of joint torques or angular velocities based on different performance requirements. This paper presents a kind of new recurrent neural networks taking joint torques and angular velocities simultaneously into consideration and proposes mid-value CLVI-PDNN to achieve the optimal joint torques and angular velocities with physical constraints of the mechanism as described in our previous paper. Because the continuous mid-value CLVI-PDNN has difficulty in real-time operation because of too much calculation workload, two kinds of methods are proposed to discretize the mid-value CLVI-PDNN for application on computer or digital circuit. The simulation results demonstrate the efficacy of the algorithm proposed in this paper.

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Continuous and discrete time Zhang dynamics for time-varying 4th root finding

Cited by 24 publications

References 17 publications

A zeroing neural network for solving discrete time-varying minimization with different adjustable parameter

A zeroing neural network for solving discrete time-varying minimization with different adjustable parameter

Relationship between time-instant number and precision of ZeaD formulas with proofs

Discretized Mid‐Value CLVI‐PDNN Based Redundancy Resolution for Single Leg of Quadruped Robot

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