A new approach to stability of neural networks with time-varying delays

Composite dynamic movement primitives based on neural networks for human–robot skill transfer

In this paper, composite dynamic movement primitives (DMPs) based on radial basis function neural networks (RBFNNs) are investigated for robots’ skill learning from human demonstrations. The composite DMPs could encode the position and orientation manipulation skills simultaneously for human-to-robot skills transfer. As the robot manipulator is expected to perform tasks in unstructured and uncertain environments, it requires the manipulator to own the adaptive ability to adjust its behaviours to new situations and environments. Since the DMPs can adapt to uncertainties and perturbation, and spatial and temporal scaling, it has been successfully employed for various tasks, such as trajectory planning and obstacle avoidance. However, the existing skill model mainly focuses on position or orientation modelling separately; it is a common constraint in terms of position and orientation simultaneously in practice. Besides, the generalisation of the skill learning model based on DMPs is still hard to deal with dynamic tasks, e.g., reaching a moving target and obstacle avoidance. In this paper, we proposed a composite DMPs-based framework representing position and orientation simultaneously for robot skill acquisition and the neural networks technique is used to train the skill model. The effectiveness of the proposed approach is validated by simulation and experiments.

Exponential stability of delayed and impulsive cellular neural networks with partially Lipschitz continuous activation functions

The paper discusses exponential stability of distributed delayed and impulsive cellular neural networks with partially Lipschitz continuous activation functions. By relative nonlinear measure method, some novel criteria are obtained for the uniqueness and exponential stability of the equilibrium point. Our method abandons usual assumptions on global Lipschitz continuity, boundedness and monotonicity of activation functions. Our results are generalization and improvement of some existing ones. Finally, two examples and their simulations are presented to illustrate the correctness of our analysis.

Multiple Almost Periodic Solutions in Nonautonomous Delayed Neural Networks

A general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed. We consider a general class of nonautonomous neural networks with delays and various activation functions. A geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed. We further derive criteria under which the n-neuron network admits 2n exponentially stable sets. In addition, we establish the existence of 2n exponentially stable almost periodic solutions for the system, when the connection strengths, time lags, and external bias are almost periodic functions of time, through applying the contraction mapping principle. Finally, three numerical simulations are presented to illustrate our theory.

Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli

This paper presents new theoretical results on the global exponential stability of recurrent neural networks with bounded activation functions and bounded time-varying delays in the presence of strong external stimuli. It is shown that the Cohen-Grossberg neural network is globally exponentially stable, if the absolute value of the input vector exceeds a criterion. As special cases, the Hopfield neural network and the cellular neural network are examined in detail. In addition, it is shown that criteria herein, if partially satisfied, can still be used in combination with existing stability conditions. Simulation results are also discussed in two illustrative examples.

Dynamics of neural networks with variable coefficients and time-varying delays

This paper studies the general neural networks dynamical systems with variable coefficients and time-varying delays. By applying the Young inequality technique, Dini derivative and introducing many real parameters, and estimating the upper bound of solutions of the system, a series of new and useful criteria on the boundedness, global exponential stability and the existence and global exponential stability of the periodic solutions are established. Particularly, when the system degenerates into the autonomous case, the new criteria on the existence, uniqueness and global exponential stability of the equilibrium points are obtained. The results obtained in this paper extend and generalize the corresponding results existing in previous literature.

Improved conditions for global exponential stability of recurrent neural networks with time-varying delays

This paper presents new theoretical results on global exponential stability of recurrent neural networks with bounded activation functions and time-varying delays. The stability conditions depend on external inputs, connection weights, and time delays of recurrent neural networks. Using these results, the global exponential stability of recurrent neural networks can be derived, and the estimated location of the equilibrium point can be obtained. As typical representatives, the Hopfield neural network (HNN) and the cellular neural network (CNN) are examined in detail.

Exponential Stability of Impulsive High-Order Hopfield-Type Neural Networks With Time-Varying Delays

This paper considers the problems of global exponential stability and exponential convergence rate for impulsive high-order Hopfield-type neural networks with time-varying delays. By using the method of Lyapunov functions, some sufficient conditions for ensuring global exponential stability of these networks are derived, and the estimated exponential convergence rate is also obtained. As an illustration, an numerical example is worked out using the results obtained.

Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays

In this paper, a general class of recurrent neural networks with time-varying delays is studied. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point and the existence of periodic solutions for such delayed neural networks. Comparing with some previous literature, in which the time-varying delays were assumed to be differentiable and their derivatives were simultaneously required to be not greater than 1, the restrictions on the time-varying delays are removed. Therefore, our results obtained here improve and extend some previously related results. Finally, two numerical examples are provided to illustrate our theorems.

Global eponential stability of cellular neural networks with time-varying coefficients and delays

In this paper, a class of cellular neural networks with time-varying coefficients and delays is considered. By constructing a suitable Liapunov functional and utilizing the technique of matrix analysis, some new sufficient conditions on the global exponential stability of solutions are obtained. The results obtained in this paper improve and extend some of the previous results.

Absolutely exponential stability of a class of neural networks with unbounded delay

In this paper, the existence and uniqueness of the equilibrium point and absolute stability of a class of neural networks with partially Lipschitz continuous activation functions are investigated. The neural networks contain both variable and unbounded delays. Using the matrix property, a necessary and sufficient condition for the existence and uniqueness of the equilibrium point of the neural networks is obtained. By constructing proper vector Liapunov functions and nonlinear integro-differential inequalities involving both variable delays and unbounded delay, using M-matrix theory, sufficient conditions for absolutely exponential stability are obtained.

Back-propagation learning of infinite-dimensional dynamical systems

This paper presents numerical studies of applying back-propagation learning to a delayed recurrent neural network (DRNN). The DRNN is a continuous-time recurrent neural network having time delayed feedbacks and the back-propagation learning is to teach spatio-temporal dynamics to the DRNN. Since the time-delays make the dynamics of the DRNN infinite-dimensional, the learning algorithm and the learning capability of the DRNN are different from those of the ordinary recurrent neural network (ORNN) having no time-delays. First, two types of learning algorithms are developed for a class of DRNNs. Then, using chaotic signals generated from the Mackey-Glass equation and the Rössler equations, learning capability of the DRNN is examined. Comparing the learning algorithms, learning capability, and robustness against noise of the DRNN with those of the ORNN and time delay neural network, advantages as well as disadvantages of the DRNN are investigated.

Global convergence of delayed neural network systems

In this paper, without assuming the boundedness, strict monotonicity and differentiability of the activation functions, we utilize a new Lyapunov function to analyze the global convergence of a class of neural networks models with time delays. A new sufficient condition guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point is derived. This stability criterion imposes constraints on the feedback matrices independently of the delay parameters. The result is compared with some previous works. Furthermore, the condition may be less restrictive in the case that the activation functions are hyperbolic tangent.