A Neural Network with Finite-Time Convergence for a Class of Variational Inequalities

Gao, Xingbao; Du, Lizhi

doi:10.1007/11816157_4

Cited by 11 publications

(17 citation statements)

References 8 publications

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“…Because Q is positive semidefinite only and many neural networks including the SDNN used in [3] can not be applied. But according to [18], this problem can be formulated into an equivalent generalized linear variational inequality, and as a consequence, it can be solved by the general projection neural network (GPNN) studied extensively in [14], [15], [19]. When specialized to solve (1) the GPNN's dynamic equation is as follows (cf.…”

Section: Neural Network Modelsmentioning

confidence: 99%

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Motion planning with obstacle avoidance for kinematically redundant manipulators based on two recurrent neural networks

Wang

Zhang

2009

2009 IEEE International Conference on Systems, Man and Cybernetics

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Abstract-Inverse kinematic motion planning of redundant manipulators by using recurrent neural networks in the presence of obstacles and uncertainties is a real-time nonlinear optimization problem. To tackle this problem, two subproblems should be resolved in real time. One is the determination of critical points on a given manipulator closest to obstacles, and the other is the computation of joint velocities of the manipulator which can direct the manipulator following a desired trajectory and away from obstacles if it is getting close to them. Different from our previous approaches where the critical points on the manipulator were assumed to be known, these points are to be computed by using a recurrent neural network in the paper. A time-varying quadratic programming problem is formulated for avoiding polyhedral obstacles. In view that the problem is not strictly convex, an existing recurrent neural network, general projection neural network, is applied for solving it. By introducing a velocity smoothing technique into our previous quadratic programming formulation of the joint velocity assignment problem, a recently developed recurrent neural network, improved dual neural network, is proposed to solve it, which features lower structural complexity compared with existing neural networks. Moreover, The effectiveness of the proposed neural networks is demonstrated by simulations on the Mitsubishi PA10-7C manipulator.

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Section: Neural Network Modelsmentioning

confidence: 99%

“…The architecture of the neural network can be drawn similarly as in [19] or [15], which is omitted here for brevity. Since Q is positive semidefinite, according to [18], the neural network is globally asymptotically convergent to a solution of (1).…”

Section: Neural Network Modelsmentioning

confidence: 99%

Motion planning with obstacle avoidance for kinematically redundant manipulators based on two recurrent neural networks

Wang

Zhang

2009

2009 IEEE International Conference on Systems, Man and Cybernetics

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“…Based on the projection NN model (2), the following NN model was developed for solving GLVIs when is a box set [16], [17]: (5) However, in applications, is often a polyhedron defined by a set of linear equalities and inequalities. Other than some refined NN models for solving generally constrained LVIs (e.g., see [10]), no NN has been proposed for solving generally constrained GLVIs.…”

Section: Inear Variational Inequality (Lvi) Is To Findmentioning

confidence: 99%

Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks

Wang

2007

IEEE Trans. Neural Netw.

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“…where λ > 0, α > 0, W ∈ (m+h+r)×(m+h+r) are constants, u = (x T , y T ) T is the state vector, and PŨ (·) is the activation function defined similarly as in (4). The output of the neural network is simply x(t), the first part of the state u(t).…”

Section: General Constraintsmentioning

confidence: 99%

“…where x and x are constants (without loss of generality, any component of x or −x can be −∞), a neurodyamic approach was proposed in [4] and [5] from different viewpoints for solving it. Moreover, in [5], the neurodynamic system was given a name, general projection neural network (GPNN).…”

Section: Introductionmentioning

confidence: 99%

Three Global Exponential Convergence Results of the GPNN for Solving Generalized Linear Variational Inequalities

Zeng

Zhang

Lecture Notes in Computer Science

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Abstract. The general projection neural network (GPNN) is a versatile recurrent neural network model capable of solving a variety of optimization problems and variational inequalities. In a recent article [IEEE Trans. Neural Netw., 18(6), 1697-1708, the linear case of GPNN was studied extensively from the viewpoint of stability analysis, and it was utilized to solve the generalized linear variational inequality with various types of constraints. In the present paper we supplement three global exponential convergence results for the GPNN for solving these problems. The first one is different from those shown in the original article, and the other two are improved versions of two results in that article. The validity of the new results are demonstrated by numerical examples.

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A Neural Network with Finite-Time Convergence for a Class of Variational Inequalities

Cited by 11 publications

References 8 publications

Motion planning with obstacle avoidance for kinematically redundant manipulators based on two recurrent neural networks

Motion planning with obstacle avoidance for kinematically redundant manipulators based on two recurrent neural networks

Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks

Three Global Exponential Convergence Results of the GPNN for Solving Generalized Linear Variational Inequalities

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