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This paper presents a novel recurrent neural network for solving nonlinear optimization problems with inequality constraints. Under the condition that the Hessian matrix of the associated Lagrangian function is positive semidefinite, it is shown that the proposed neural network is stable at a Karush-Kuhn-Tucker point in the sense of Lyapunov and its output trajectory is globally convergent to a minimum solution. Compared with variety of the existing projection neural networks, including their extensions and modification, for solving such nonlinearly constrained optimization problems, it is shown that the proposed neural network can solve constrained convex optimization problems and a class of constrained nonconvex optimization problems and there is no restriction on the initial point. Simulation results show the effectiveness of the proposed neural network in solving nonlinearly constrained optimization problems. Index Terms--Global convergence, nonconvex programming, nonlinear inequality constraints, nonsmooth analysis, recurrent neural network.

This paper proposes a generalized least absolute deviation (GLAD) method for parameter estimation of autoregressive (AR) signals under non-Gaussian noise environments. The proposed GLAD method can improve the accuracy of the estimation of the conventional least absolute deviation (LAD) method by minimizing a new cost function with parameter variables and noise error variables. Compared with second- and high-order statistical methods, the proposed GLAD method can obtain robustly an optimal AR parameter estimation without requiring the measurement noise to be Gaussian. Moreover, the proposed GLAD method can be implemented by a cooperative neural network (NN) which is shown to converge globally to the optimal AR parameter estimation within a finite time. Simulation results show that the proposed GLAD method can obtain more accurate estimates than several well-known estimation methods in the presence of different noise distributions. Index Terms--Autoregressive (AR) parameter estimation, generalized least absolute deviation (GLAD) method, neural network (NN) algorithm, non-Gaussian noise environments.

This technical note develops a neural dynamical approach to nonlinear programming (NP) problems, whose equilibrium points coincide with Karush-Kuhn-Tucker points of the NP problem. A rigorous analysis on the global convergence and the convergence rate of the proposed neural dynamical approach is carried out under the condition that the associated Lagrangian function is convex. Analysis results show that the proposed neural dynamical approach can solve general convex programming problems and a class of nonconvex programming problems. Two nonconvex programming examples are provided to demonstrate the performance of the developed neural dynamical approach. Index Terms--Global convergence, neural dynamical optimization approach, nonconvex programming.

The problem of spatial-temporal signal processing and modeling has been of great interest in recent years. A new spatial-temporal prediction method is presented in this paper. An optimal fusion scheme based on fourth-order statistic is first employed to combine the received signals at different spatial domains. The fused signal is then used to construct a spatial-temporal predictor by a support vector machine. It is shown theoretically that the proposed method has an improved performance even in non-Gaussian environments. To demonstrate the practicality of this spatial-temporal predictor, we apply it to model real-life radar sea scattered signals. Experimental results show that the proposed method can provide a more accurate model for sea clutter than the conventional methods. Index Terms--Chaos, data fusion, prediction, radar, spatial-temporal signal processing, support vector machine (SVM).

In this paper, we propose a new spatial temporal predictor using support vector machine (SVM) and data fusion technique. SVMs are used as temporal predictors at different spatial domains and spatial temporal prediction is achieved by prediction fusion. Our proposed prediction fusion technique improves the prediction accuracy even in a non-Gaussian environment. The performance of the proposed spatial temporal predictor is analyzed. Based on real-life radar data, the proposed spatial temporal approach is shown to provide a more accurate model for sea-clutter data than the conventional methods. Index Terms--Data fusion, neural networks, nonlinear dynamics, prediction, signal modeling, spatial temporal dynamics, support vector machine (SVM).

In this paper, we present a delayed neural network approach to solve linear projection equations. The Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network. Compared with the existing linear projection neural network, theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems. Index Terms--Asymptotical stability, delayed neural networks, exponential stability, linear matrix inequality (LMI), Lyapunov-Krasovskii functional, quadratic programming.

In this paper, we propose a recurrent neural network for solving nonlinear convex programming problems with linear constraints. The proposed neural network has a simpler structure and a lower complexity for implementation than the existing neural networks for solving such problems. It is shown here that the proposed neural network is stable in the sense of Lyapunov and globally convergent to an optimal solution within a finite time under the condition that the objective function is strictly convex. Compared with the existing convergence results, the present results do not require Lipschitz continuity condition on the objective function. Finally, examples are provided to show the applicability of the proposed neural network. Index Terms--Continuous methods, global convergence, linear constraints, recurrent neural networks, strictly convex programming.

This paper proposes a primal-dual neural network with a one-layer structure for online resolution of constrained kinematic redundancy in robot motion control. Unlike the Lagrangian network, the proposed neural network can handle physical constraints, such as joint limits and joint velocity limits. Compared with the existing primal-dual neural network, the proposed neural network has a low complexity for implementation. Compared with the existing dual neural network, the proposed neural network has no computation of matrix inversion. More importantly, the proposed neural network is theoretically proved to have not only a finite time convergence, but also an exponential convergence rate without any additional assumption. Simulation results show that the proposed neural network has a faster convergence rate than the dual neural network in effectively tracking for the motion control of kinematically redundant manipulators. Index Terms--Constrained kinematic redundancy, joints limits, joint velocity, primal-dual neural network.

This paper presents a novel recurrent neural network for solving nonlinear convex programming problems subject to nonlinear inequality constraints. Under the condition that the objective function is convex and all constraint functions are strictly convex or that the objective function is strictly convex and the constraint function is convex, the proposed neural network is proved to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution. Compared with the existing neural networks for solving such nonlinear optimization problems, the proposed neural network has two major advantages. One is that it can solve convex programming problems with general convex inequality constraints. Another is that it does not require a Lipschitz condition on the objective function and constraint function. Simulation results are given to illustrate further the global convergence and performance of the proposed neural network for constrained nonlinear optimization. Index Terms--Continuous method, convex programming, global convergence, recurrent neural networks.

Grasping-force optimization of multifingered robotic hands can be formulated as a problem for minimizing an objective function subject to form-closure constraints and balance constraints of external force. This paper presents a novel recurrent neural network for real-time dextrous hand-grasping force optimization. The proposed neural network is shown to be globally convergent to the optimal grasping force. Compared with existing approaches to grasping-force optimization, the proposed neural-network approach has the advantages that the complexity for implementation is reduced, and the solution accuracy is increased, by avoiding the linearization of quadratic friction constraints. Simulation results show that the proposed neural network can achieve optimal grasping force in real time. Index Terms--Grasping-force optimization, multifingered robotic hands, recurrent neural networks.

This paper presents a one-layer recurrent neural network for support vector machine (SVM) learning in pattern classification and regression. The SVM learning problem is first converted into an equivalent formulation, and then a one-layer recurrent neural network for SVM learning is proposed. The proposed neural network is guaranteed to obtain the optimal solution of support vector classification and regression. Compared with the existing two-layer neural network for the SVM classification, the proposed neural network has a low complexity for implementation. Moreover, the proposed neural network can converge exponentially to the optimal solution of SVM learning. The rate of the exponential convergence can be made arbitrarily high by simply turning up a scaling parameter. Simulation examples based on benchmark problems are discussed to show the good performance of the proposed neural network for SVM learning. Index Terms--Exponential convergence, quadratic programming, recurrent neural networks, support vector machines.

Recently, a projection neural network for solving monotone variational inequalities and constrained optimization problems was developed. In this paper, we propose a general projection neural network for solving a wider class of variational inequalities and related optimization problems. In addition to its simple structure and low complexity, the proposed neural network includes existing neural networks for optimization, such as the projection neural network, the primal-dual neural network, and the dual neural network, as special cases. Under various mild conditions, the proposed general projection neural network is shown to be globally convergent, globally asymptotically stable, and globally exponentially stable. Furthermore, several improved stability criteria on two special cases of the general projection neural network are obtained under weaker conditions. Simulation results demonstrate the effectiveness and characteristics of the proposed neural network. Index Terms--Global stability, recurrent neural networks, variational inequalities optimization.

This note presents an analysis of the convergence rate for a projection neural network with application to constrained optimization and related problems. It is shown that the state trajectory of the projection neural network is exponentially convergent to its equilibrium point if the Jacobian matrix of the nonlinear mapping is positive definite, while the convergence rate is proportional to a design parameter if the Jacobian matrix is only positive semidefinite. Moreover, the convergence time is guaranteed to be finite if the design parameter is chosen to be sufficiently large. Furthermore, if a diagonal block of the Jacobian matrix is positive definite, then the corresponding partial state trajectory of the projection neural network is also exponentially convergent. Three optimization examples are used to show the convergence performance of the projection neural network. Index Terms--Convergence rate, convergence time, projection neural network.

Many models arisen in signal and image processing can be formulated as a nonlinear convex programming problem with linear equality constraints. A Lagrangian network was developed for real-time applications of these problems. Yet, the global convergence of the Lagrangian network has not been well studied due to the asymmetry of the corresponding Lagrange system. In this brief, based on a new Lyapunov function we analyze and prove the global convergence of the Lagrangian network. Simulation examples are provided to show the effectiveness of the obtained results. Index Terms--Asymmetry, global convergence, Lagrange system.

In this paper, a recurrent neural network called the dual neural network is proposed for online redundancy resolution of kinematically redundant manipulators. Physical constraints such as joint limits and joint velocity limits, together with the drift-free criterion as a secondary task, are incorporated into the problem formulation of redundancy resolution. Compared to other recurrent neural networks, the dual neural network is piecewise linear and has much simpler architecture with only one layer of neurons. The dual neural network is shown to be globally (exponentially) convergent to optimal solutions. The dual neural network is simulated to control the PAIO robot manipulator with effectiveness demonstrated. Index Terms--Drift-free, dual neural network, joint limits, joint velocity limits, kinematically redundant manipulators.