RNN for Solving Perturbed Time-Varying Underdetermined Linear System With Double Bound Limits on Residual Errors and State Variables

Lu, Huosheng; Jin, Long; Luo, Xin; Liao, Bolin; Guo, Dongsheng; Xiao, Lin

doi:10.1109/tii.2019.2909142

Cited by 141 publications

(51 citation statements)

References 30 publications

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“…That is, solving time-variant Sylvester equation 1is equivalently transformed into forcing E(t) converging to 0. Then, to make the error function (2) decrease to 0, the following ZNN design formula is employed [21], [22], [26]:…”

Section: A Znn Modelmentioning

confidence: 99%

New Noise-Tolerant ZNN Models With Predefined-Time Convergence for Time-Variant Sylvester Equation Solving

Xiao

Zhang

Dai

et al. 2021

IEEE Trans. Syst. Man Cybern, Syst.

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Sylvester equation is often applied to various fields such as mathematics and control systems due to its importance. Zeroing neural network (ZNN), as a systematic design method for time-variant problems, has been proved to be effective on solving Sylvester equation in the ideal conditions. In this work, in order to realize the predefined-time convergence of the ZNN model and modify its robustness, two new noise-tolerant zeroing neural networks (NNTZNNs) are established by devising two novelly constructed nonlinear activation functions (AFs) to find the accurate solution of time-variant Sylvester equation in the presence of various noises. Unlike the original ZNN models activated by known AFs, the proposed two NNTZNN models are activated by two novel AFs, therefore possessing the excellent predefined-time convergence and strong robustness even in the presence of various noises. Besides, the detailed theoretical analyses of the predefinedtime convergence and robustness ability for the NNTZNN models are given by considering different kinds of noises. Simulation comparative results further verify the excellent performance of the proposed NNTZNN models, when applied to online solution of time-variant Sylvester equation. Index Terms-Zeroing neural network (ZNN), finite-time convergence, nonlinear activation function, Sylvester equation, timevariant problems. I. INTRODUCTION S OLVING Sylvester equation is often found in mathematics and control theory and applied to solve various important problems such as eigenvalue assignment [1], and image processing [2]. Therefore, it is a crucial issue to solve Sylvester equation by designing various different schemes. Numerical methods were usually used to solve the static Sylvester equation in the past [3]-[14], such as Bartels-Stewart, and Hessenberg-Schur iteration methods [8]-[14].

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Section: A Znn Modelmentioning

confidence: 99%

New Noise-Tolerant ZNN Models With Predefined-Time Convergence for Time-Variant Sylvester Equation Solving

Xiao

Zhang

Dai

et al. 2021

IEEE Trans. Syst. Man Cybern, Syst.

Self Cite

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“…Let P −1 i = X i and Y i = X i L pi , the above inequality is rewritten as (10), and the observer gain can be designed as…”

Section: Observer Design Based On Sliding Mode Controlmentioning

confidence: 99%

“…By using replacement of matrix variables, a new mean square admissibility criterion of singular stochastic Markov systems was proposed first in [4]. In [10], the authors proposed a novel recurrent neural network (RNN) to handle the perturbed time-varying underdetermined linear system with double bound limits on residual errors and state vari-…”

Section: Introductionmentioning

confidence: 99%

Observer-Based Finite-Time Adaptive Sliding Mode Control for Itô Stochastic Jump Systems With Actuator Degradation

2020

IEEE Access

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This paper investigates the problem of finite-time adaptive sliding mode control for Itô stochastic systems with Markovian switching, where the transition rate matrix of the jump systems is partially available, and unknown actuator degradation factors and matched nonlinearity are considered simultaneously. In this design, an adaptive sliding mode observer is first proposed for the investigated plant to reconstruct the system state, where effects of actuator degradations are compensated by the observer with the adaptive estimation mechanism. Based on the state estimation, an observer-based adaptive sliding mode control law is developed to stabilize the overall closed-loop system, which can also ensure the state trajectories to be driven onto the sliding surface in finite-time with a pre-specified finite-time interval. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed fault tolerant control methodology. INDEX TERMS Itô stochastic jump systems, actuator degradation factor, sliding mode control, sliding mode observer.

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“…The existing studies may be flawed to some extent. For example, in [36], an RNN for solving the perturbed dynamic linear system with double-bound limits on joint velocity is applied to a physically-limited PUMA 560 robot in tracking trajectory satisfactorily, which is a continuous-time model. In addition, another neural network in the continuous form is developed in [37] for robots to realize repetitive motion generation with equality and inequality constraints but the perturbations are ignored.…”

Section: Introductionmentioning

confidence: 99%

Discrete Perturbation-Immunity Neural Network for Dynamic Constrained Redundant Robot Control

Yang

Chen

et al. 2020

IEEE Access

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Considering the necessity of merging the physical constraints in joint space for redundant robot motion control in practice by regarding the kinematics of robots, a discrete perturbation-immunity neural network (DPINN) model with high robustness and predominant convergence is proposed in this article for managing the problem. It is worth emphasizing that this proposed neural network is developed to provide a solution algorithm to dispose of the practical applications in robot motion control that is investigated by reforming it into perturbed dynamic quadratic programming (QP) with equality and inequality constraints, which remedies the lack and drawbacks of existing methodologies. Moreover, theoretical verifications and results verify the convergence performance and noise suppression ability of the proposed neural network, which is further verified by simulation examples. In addition, the simulations on robot motion control embody its superiority and powerful versatility compared to the existing methods. In summary, the proposed neural network extends the sphere of application in perturbed dynamic QP with double-bound constraints and offers a feasible scheme capable of controlling robots in a neural-network thought. INDEX TERMS Discrete perturbation-immunity neural network (DPINN), physical constraints, robots, theoretical verifications.

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RNN for Solving Perturbed Time-Varying Underdetermined Linear System With Double Bound Limits on Residual Errors and State Variables

Cited by 141 publications

References 30 publications

New Noise-Tolerant ZNN Models With Predefined-Time Convergence for Time-Variant Sylvester Equation Solving

New Noise-Tolerant ZNN Models With Predefined-Time Convergence for Time-Variant Sylvester Equation Solving

Observer-Based Finite-Time Adaptive Sliding Mode Control for Itô Stochastic Jump Systems With Actuator Degradation

Discrete Perturbation-Immunity Neural Network for Dynamic Constrained Redundant Robot Control

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