The Lyapunov equation is widely employed in the engineering field to analyze stability of dynamic systems. In this paper, based on a new evolution formula, novel finite-time recurrent neural network (termed Zhang network, FTZNN) proposed and studied for solving nonstationary equation. comparison with original (ZNN) model equation, convergence performance has remarkable improvement FTZNN can be accelerated finite time. Besides, by differential inequality, time upper bound computed...

Using neural networks to handle intractability problems and solve complex computation equations is becoming common practices in academia industry. It has been shown that, although complicated, these can be formulated as a set of the key find zeros them. Zeroing (ZNN), class particularly dedicated equations, have played an indispensable role online solution time-varying problem past years many fruitful research outcomes reported literatures. The aim this paper provide comprehensive survey on...

Neural networks have been generally deemed as important tools to handle kinds of online computing problems in recent decades, which plenty applications science and electronics fields. This paper proposes a novel recurrent neural network (RNN) the perturbed time-varying underdetermined linear system with double bound limits on residual errors state variables. Beyond that, bound-limited is converted into that consists nonlinear formulas through constructing nonnegative variable. Then,...

In this paper, a distributed scheme is proposed for the cooperative motion generation in network of multiple redundant manipulators. The can simultaneously achieve specified primary task to reach global cooperation under limited communications among manipulators and optimality terms optimization index robot reformulated as quadratic program (QP). To inherently suppress noises originating from communication interferences or computational errors, noise-tolerant zeroing neural (NTZNN)...

As a special class of recurrent neural network, Zhang network (ZNN) has been recently proposed since 2001 for solving various time-varying problems, and shown high efficiency excellent performance the problems in real domain. In this paper, to solve online complex generalized inverse (in most cases, pseudoinverse) problem domain, new type complex-valued ZNN is further investigated. The design such based on function (ZF) which indefinite quite different from usual error (specially,...

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on formula, two discrete-time ZNN models (termed ZNNK ZNNU models) are then proposed discussed perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type (called Newton iteration, with interesting links being found, also presented. It proved herein that...

Input disturbances and physical constraints are important issues in the kinematic control of redundant manipulators. In this paper, we propose a novel recurrent neural network to simultaneously address periodic input disturbance, joint angle constraint, velocity optimize general quadratic performance index. The proposed applies both regulation tracking tasks. Theoretical analysis shows that, with network, end-effector errors asymptotically converge zero presence disturbance two constraints....

Varying-parameter recurrent neural network, being a special kind of neural-dynamic methodology, has revealed powerful abilities to handle various time-varying problems, such as quadratic minimization (QM) and programming (QP) problems. In this paper, novel power-type varying-parameter network (PT-VP-RNN) is proposed solve the perturbed QM QP First, based on generalization design process PT-VP-RNN presented in detail. Second, robustness performance theoretically analyzed proved. What more,...

The so-called zeroing neural network (ZNN) is an effective recurrent for solving dynamic problems including the nonlinear equations. There exist numerous unperturbed ZNN models that can converge to theoretical solution of solvable equations in infinity long or finite time. However, when these are perturbed by external disturbances, convergence performance would be dramatically deteriorated. To overcome this issue, paper first time proposes a finite-time convergent with noise-rejection...

As a type of recurrent neural networks (RNNs) modeled as dynamic systems, the gradient network (GNN) is recognized an effective method for static matrix inversion with exponential convergence. However, when it comes to time-varying inversion, most traditional GNNs can only track corresponding solution residual error, and performance becomes worse there are noises. Currently, zeroing (ZNNs) take dominant role in but ZNN models more complex than GNN models, require knowing explicit formula...

Abstract In engineering fields, time‐varying matrix inversion (TVMI) issue is often encountered. Zeroing neural network (ZNN) has been extensively employed to resolve the TVMI problem. Nevertheless, original ZNN (OZNN) and integral‐enhanced (IEZNN) usually fail deal with problem under unbounded noises, such as linear noises. Therefore, a model that can handle noise interference urgently needed. This paper develops double (DIEZNN) based on novel integral‐type design formula inherent...

Computing time-varying linear systems is widely encountered in engineering practice and scientific computation. Dynamic neural networks, as a class of modeling approaches, have been intensively explored recent decades for solving equations. The nature this problem the noisy workspace many require two features practical design: 1) fast convergence time 2) robustness against noises disturbance. Existing solutions usually decouple into steps by designing fast-convergent controller then topped...

SUMMARY In this paper, a pseudoinverse-type bi-criteria minimization scheme is proposed and investigated for the redundancy resolution of robot manipulators at joint-acceleration level. Such combines weighted minimum acceleration norm solution velocity via weighting factor. The resultant scheme, formulated as solution, not only avoids high joint-velocity phenomena but also causes joint to be near zero end motion. Computer simulation results based on 4-Degree-of-Freedom planar manipulator...

Time-varying problems are prevalent in engineering, presenting a significant challenge due to the fluctuations parameters and goals at different time points. The Zeroing Neural Network (ZNN), specialized form of Recurrent (RNN) developed by Zhang et al., has gained attention for its rapid convergence speed robustness making it valuable tool real-time solving diverse time-varying problems. This review article explores practical applications ZNN across various domains past two decades,...

Repetitive motion planning (RMP) is a crucial issue encountered in studies on redundant robot manipulators. Numerous RMP schemes have been established previous wherein simulations are assumed to be free of noise. However, noise ubiquitous and can severely affect the point causing failure. This paper attempts address limitations imposed by providing first scheme with inherent noise-suppression capability. The new for manipulators noisy environment proposed basis an equality criterion that...