A Recurrent Neural Network for Solving a Class of General Variational Inequalities

Hu, Xiaolin; Wang, Jun

doi:10.1109/tsmcb.2006.886166

Cited by 71 publications

(26 citation statements)

References 28 publications

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“…Theoretically, the -WTA network (21) as well as network (18) do not need to choose any parameter (the scaling factor can be any positive number), which can be deemed as a great advantage over networks (15) and (16). In addition, the two networks (18) and (21) allow for some equal input signals [see (17)], a situation often encountered in practice but excluded by (15) and (16).…”

Section: Model Comparisonsmentioning

confidence: 99%

“…In addition, the two networks (18) and (21) allow for some equal input signals [see (17)], a situation often encountered in practice but excluded by (15) and (16). These facts have been indicated in the last two rows of Table II for a clear comparison.…”

Section: Model Comparisonsmentioning

confidence: 99%

“…This is an ill case of the -WTA problem, but in many applications, it cannot be avoided. Obviously, in this case, there is no way to choose a proper for the network (16).…”

Section: A Introductionmentioning

confidence: 99%

“…Recently, another -WTA network was devised, which can conquer the difficulties encountered by (16), [42]:…”

Section: A Introductionmentioning

confidence: 99%

“…Moreover, in view of its formulation in [42] and the analysis in Section III-B, it is easy to see that in the ill case of (17), the network still works. The disadvantage is its relatively complicated structure in contrast to (16). In what follows, we design a simpler network while its merits are retained.…”

Section: A Introductionmentioning

confidence: 99%

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A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem

Zhang

2009

IEEE Trans. Neural Netw.

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Abstract-In this paper, a new recurrent neural network is proposed for solving convex quadratic programming (QP) problems. Compared with existing neural networks, the proposed one features global convergence property under weak conditions, low structural complexity, and no calculation of matrix inverse. It serves as a competitive alternative in the neural network family for solving linear or quadratic programming problems. In addition, it is found that by some variable substitution, the proposed network turns out to be an existing model for solving minimax problems. In this sense, it can be also viewed as a special case of the minimax neural network. Based on this scheme, a -winners-take-all ( -WTA) network with ( ) complexity is designed, which is characterized by simple structure, global convergence, and capability to deal with some ill cases. Numerical simulations are provided to validate the theoretical results obtained. More importantly, the network design method proposed in this paper has great potential to inspire other competitive inventions along the same line. IndexTerms-Asymptotic stability, -winners-take-all ( -WTA), linear programming, neural network, quadratic programming.

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Section: Model Comparisonsmentioning

confidence: 99%

Section: Model Comparisonsmentioning

confidence: 99%

“…This is an ill case of the -WTA problem, but in many applications, it cannot be avoided. Obviously, in this case, there is no way to choose a proper for the network (16).…”

Section: A Introductionmentioning

confidence: 99%

“…Recently, another -WTA network was devised, which can conquer the difficulties encountered by (16), [42]:…”

Section: A Introductionmentioning

confidence: 99%

Section: A Introductionmentioning

confidence: 99%

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A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem

Zhang

2009

IEEE Trans. Neural Netw.

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Optimal sliding‐mode control of linear systems with uncertainties and input constraints using projection neural network

Toshani

Farrokhi

2017

Optim Control Appl Methods

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Summary In this paper, an optimal sliding‐mode control (SMC) method based on the projection recurrent neural networks for a class of linear systems with uncertainties and input constraint is developed. The chattering in the SMC is eliminated by introducing a performance index for minimizing the sliding‐surface variations and the control effort. Moreover, the constraints on the actuators are considered in the optimization problem, which is solved using projection recurrent neural network. The main advantages of the proposed method are obtaining an optimal and chattering‐free control law in a feasible space. Moreover, the parameters of the proposed control method are determined based on the closed‐loop stability and robustness analysis. The performance of the proposed method is evaluated by considering uncertainties and input constraints in the system and is compared with the conventional and a second‐order SMC in the view of chattering, input saturation, and robustness.

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Lagrange Programming Neural Network for the $$l_1$$ -norm Constrained Quadratic Minimization

Lee

Feng

Leung

2015

Neural Information Processing

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A Recurrent Neural Network for Solving a Class of General Variational Inequalities

Cited by 71 publications

References 28 publications

A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem

A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem

Optimal sliding‐mode control of linear systems with uncertainties and input constraints using projection neural network

Lagrange Programming Neural Network for the $$l_1$$ -norm Constrained Quadratic Minimization

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