Complex ZNN for computing time-varying weighted pseudo-inverses

Stanimirović, Stefan; Wang, Xuezhong; Ma, Haifeng

doi:10.2298/aadm170628019s

Cited by 5 publications

(2 citation statements)

References 42 publications

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“…The right pseudoinverse code for full rank matrix flows is similar. Recent work on pseudo-inverses has appeared in [13] and [31, chapters 8,9].…”

Section: Part B : Some Applications For Znn Methodsmentioning

confidence: 99%

Zeroing Neural Networks, an Introduction to, a Survey of, and Predictive Computations for Discretized Time-varying Matrix Problems

Uhlig¹

2020

Preprint

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This paper is designed to increase knowledge and understanding of time-varying matrix problems and Zeroing Neural Networks in the numerical analysis community of the west. Zeroing neural networks (ZNN) were invented 20 years ago in China and almost all of their advances have been made in and still come from its birthplace. ZNN methods have become a backbone for solving discretized sensor driven timevarying matrix problems in real-time, in theory and in on-chip applications for robots, in control theory and engineering in general. They have become the method of choice for many time-varying matrix problems that benefit from or require efficient, accurate and predictive real-time computations. The typical ZNN algorithm needs seven distinct steps for its set-up. The construction of ZNN algorithms starts with an error equation and the stipulation that the error function decrease exponentially fast. The error function DE is then mated with a convergent look-ahead finite difference formula to create a derivative free computer code that predicts the future state of the system reliably from current and earlier state data. Matlab codes for ZNN typically consist of one linear equations solve and one short recursion of current and previous state data per time step. This makes ZNN based algorithms highly competitive with ODE IVP path following or homotopy methods that are not designed to work with constant sampling gap incoming sensor data but rather work adaptively. To illustrate the easy adaptability of ZNN and further the understanding of ZNN, this paper details the seven set-up steps for 11 separate time-varying problems and supplies the codes for six. Open problems are mentioned as well as detailed references to recent work on each of the treated problems.

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“…The right pseudoinverse code for full rank matrix flows is similar. Recent work on pseudo-inverses has appeared in [13] and [31, chapters 8,9].…”

Section: Part B : Some Applications For Znn Methodsmentioning

confidence: 99%

Zeroing Neural Networks, an Introduction to, a Survey of, and Predictive Computations for Discretized Time-varying Matrix Problems

Uhlig¹

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Since then, more and more researchers have joined the research on ZNN, and many elegant ZNNs with different purposes have thus come up. For example, the complex-valued ZNNs [14], the noise-tolerant ZNNs [15], and the ZNNs with finite-time convergence [16].…”

Section: Introductionmentioning

confidence: 99%

Fixed-Time, Robust and Fuzzy Adaptive Consensus Control with Event Trigger Mechanism Based on a Novel ZNN Scheme

Xiao,

Luo,

Ning

et al. 2023

Preprint

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As a systematic approach, zeroing neural network (ZNN) is an elegant tool in control applications. However, the application of ZNNs in multi-agent systems still needs further research. Adaptive control schemes with adjustable convergence speed are important in practical application, but researchers mainly use explicit and direct rules to update the convergence parameter, which is less effective than using fuzzy logic system (FLS). In this study, combined with FLS, a novel event-triggered fuzzy adaptive ZNN (ET-FAZNN) model is proposed to solve the consensus problem in a fixed time. With a set of predefined fuzzy rules, the convergence rate is adaptively adjusted after an overall evaluation of the system state. We also boost computing efficiency by introducing the event-triggered mechanism. Specifically, we first present a detailed theoretical analysis to show that the novel ET-FAZNN model is fixed-time stable and robust. Then, we estimated the upper bounds of settling-time functions through a novel method based on the improper integral. Finally, four numerical experiments are presented to further verify the fixed-time convergence, adaptiveness, robustness, and the superior computing efficiency compared with conventional fuzzy adaptive ZNN.

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Zhang neural networks: an introduction to predictive computations for discretized time-varying matrix problems

Uhlig

2024

Numer. Math.

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This paper wants to increase our understanding and computational know-how for time-varying matrix problems and Zhang Neural Networks. These neural networks were invented for time or single parameter-varying matrix problems around 2001 in China and almost all of their advances have been made in and most still come from its birthplace. Zhang Neural Network methods have become a backbone for solving discretized sensor driven time-varying matrix problems in real-time, in theory and in on-chip applications for robots, in control theory and other engineering applications in China. They have become the method of choice for many time-varying matrix problems that benefit from or require efficient, accurate and predictive real-time computations. A typical discretized Zhang Neural Network algorithm needs seven distinct steps in its initial set-up. The construction of discretized Zhang Neural Network algorithms starts from a model equation with its associated error equation and the stipulation that the error function decrease exponentially fast. The error function differential equation is then mated with a convergent look-ahead finite difference formula to create a distinctly new multi-step style solver that predicts the future state of the system reliably from current and earlier state and solution data. Matlab codes of discretized Zhang Neural Network algorithms for time varying matrix problems typically consist of one linear equations solve and one recursion of already available data per time step. This makes discretized Zhang Neural network based algorithms highly competitive with ordinary differential equation initial value analytic continuation methods for function given data that are designed to work adaptively. Discretized Zhang Neural Network methods have different characteristics and applicabilities than multi-step ordinary differential equations (ODEs) initial value solvers. These new time-varying matrix methods can solve matrix-given problems from sensor data with constant sampling gaps or from functional equations. To illustrate the adaptability of discretized Zhang Neural Networks and further the understanding of this method, this paper details the seven step set-up process for Zhang Neural Networks and twelve separate time-varying matrix models. It supplies new codes for seven of these. Open problems are mentioned as well as detailed references to recent work on discretized Zhang Neural Networks and time-varying matrix computations. Comparisons are given to standard non-predictive multi-step methods that use initial value problems ODE solvers and analytic continuation methods.

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Complex ZNN for computing time-varying weighted pseudo-inverses

Cited by 5 publications

References 42 publications

Zeroing Neural Networks, an Introduction to, a Survey of, and Predictive Computations for Discretized Time-varying Matrix Problems

Zeroing Neural Networks, an Introduction to, a Survey of, and Predictive Computations for Discretized Time-varying Matrix Problems

Fixed-Time, Robust and Fuzzy Adaptive Consensus Control with Event Trigger Mechanism Based on a Novel ZNN Scheme

Zhang neural networks: an introduction to predictive computations for discretized time-varying matrix problems

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