Some stability properties of dynamic neural networks

Journal of Industrial and Management Optimization, 2011

In this paper, by using some analytic techniques, several sufficient conditions are given to ensure the passivity of continuous-time recurrent neural networks with delays. The passivity conditions are presented in terms of some negative semi-definite matrices. They are easily verifiable and easier to check computing with some conditions in terms of complicated linear matrix inequality.

2007

This paper deals with the problem of Passivity analysis for neural networks with multiple time-varying delays subject to norm-bounded time-varying parameter uncertainties. The activation functions are supposed to be bounded and globally Lipschitz continuous. New passivity conditions are proposed by using Lyapunov-Krasovskii functionals and the free–weighting matrix method to relax the existing requirement of derivative of time delays of the system. Passivity conditions are obtained in terms of linear matrix inequalities, which can be investigated easily by using recently developed standard algorithms. Two illustrative examples are provided to demonstrate the effectiveness.

Physics Letters A, 2009

In this Letter, the passivity problem of uncertain neural networks with discrete and distributed timevarying delays is investigated. New delay-dependent conditions for this problem are obtained by using a novel Lyapunov functional together with the linear matrix inequality (LMI) approach. Numerical examples are given to show the effectiveness of our theoretical results.

2011 IEEE International Symposium on Computer-Aided Control System Design (CACSD), 2011

A framework and stability conditions are presented for the analysis of stability of three different classes of dynamic artificial neural networks: (1) neural state space models, (2) global input-output models, and (3) dynamic recurrent neural networks. The models are transformed into a standard nonlinear operator form for which linear matrix inequality-based stability analysis is applied. Theory and numerical examples are used to draw connections and make comparisons to stability conditions reported in the literature for dynamic artificial neural networks.

In this paper, we derive a sufficient condition for stability of control neural networks in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method.

Expert Systems with Applications, 1998

In this paper, the authors summarize their research related to dynahaic neural control. In particular, results on nonlinear system identification, nonlinear trajectory tracking, and input-to-state stability (ISS) of dynamic neural networks are presented. The main analysis tool utilized is the Lyapunov approach. References for the detailed demonstrations are given. We illustrate the applicability of the results by means of examples.

Proceedings of the 16th IFAC World Congress, 2005, 2005

A novel neuro adaptive control framework for discrete-time multivariable nonlinear uncertain systems is developed. The proposed framework is Lyapunov-based and guarantees, instead of ultimate boundedness, partial asymptotic stability of the closedloop system; that is, Lyapunov stability of the closed-loop system states and attraction with respect to the plant states. Unlike standard neural network approximation, we assume that the approximation error can be confined in a small gain-type norm-bounded conic sector over a compact set. This helps to couple tools from robust control with adaptive laws in discrete time to prove partial asymptotic stability of the closed-loop system. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

2014

The controllers which are built using classical methods in the process of system operation do not provide full adequacy with controlled values of nonlinear objects. We consider the features of dynamic neural network and the reference mathematical models construction which carried the review of neurons activation functions and feasibility of using gradient algorithms including the Levenberg-Marquardt algorithm for training of dynamic neural networks. Obviously the control action of such dynamic system is corresponded with the difference between output signals of the non-linear object and the chosen reference. On contrary to a typical structure it was proposed to put these signals on two separate inputs. The comparison of obtained errors in traditional and proposed structures of input circuit of neural controller showed that the last one is the most effective in quality and productivity sense. Also the stability of the system supported by neural controller with two separated inputs is...

Journal of Dynamics and Differential Equations, 1997

A stability analysis of the equilibrium position for a given class of Hopfield neural networks with time delays is presented. The robustness of the equilibrium stability with respect to variations in the time delays, system parameters, and interconnection matrix is analyzed. Three approaches are presented which account in various ways for stability of the equilibrium with respect to these perturbations.

Reports on Mathematical Physics, 2013

In this paper, we study the passivity analysis for a class of neutral-type BAM neural networks with time-varying delays and randomly occurring uncertainties as well as generalized activation functions. Linear matrix inequality (LMI) approach together with the construction of proper Lyapunov-Krasovskii functional involving triple integrals and augmented type constraint is implemented to derive a new set of sufficient conditions for obtaining the required result. More precisely, first we derive the passivity condition for BAM neural networks without uncertainties and then the result is extended to the case with randomly occurring uncertainties. In particular, the presented results depend not only upon discrete delay but also distributed time varying delay. The obtained passivity conditions are formulated in terms of linear matrix inequalities that can be easily solved by using the MATLAB-LMI toolbox. Finally, the effectiveness of the proposed passivity criterion is demonstrated through numerical example.