Design of exponential state estimators for neural networks with mixed time delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this Letter, the state estimation problem is dealt with for a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. The activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Laypunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the Alexander von Humboldt Foundation of Germany, the Natural Science Foundation of Jiangsu Education Committee of China under Grants 05KJB110154 and BK2006064, and the National Natural Science Foundation of China under Grants 10471119 and 10671172

State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this Letter, we investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to the switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov–Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grants GR/S27658/01 and EP/C524586/1, an International Joint Project sponsored by the Royal Society of the UK, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the National Natural Science Foundation of China under Grant 60774073, and the Alexander von Humboldt Foundation of Germany

Filtering for a class of nonlinear discrete-time stochastic systems with state delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this paper, the filtering problem is investigated for a class of nonlinear discrete-time stochastic systems with state delays. We aim at designing a full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically, exponentially, ultimately bounded in the mean square, for all admissible nonlinearities and time delays. First, an algebraic matrix inequality approach is developed to deal with the filter analysis problem, and sufficient conditions are derived for the existence of the desired filters. Then, based on the generalized inverse theory, the filter design problem is tackled and a set of the desired filters is explicitly characterized. A simulation example is provided to demonstrate the usefulness of the proposed design method.This work was supported in part by the EPSRC under Grants GR/S27658/01 and GR/R35018/01, the Nuffield Foundation under Grant NAL/00630/G, the William M.W. Mong Engineering Research Fund of the University of Hong Kong, and the Alexander von Humboldt Foundation of Germany, and the National Natural Science Foundation of China under Grant 60504008. Z. Wang wishes to thank Dr. H. Gao of Harbin Institute of Technology of China for helpful discussions

State estimation for jumping recurrent neural networks with discrete and distributed delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper is concerned with the state estimation problem for a class of Markovian neural networks with discrete and distributed time-delays. The neural networks have a finite number of modes, and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements, such that for all admissible time-delays, the dynamics of the estimation error is globally asymptotically stable in the mean square. An effective linear matrix inequality approach is developed to solve the neuron state estimation problem. Both the existence conditions and the explicit characterization of the desired estimator are derived. Furthermore, it is shown that the traditional stability analysis issue for delayed neural networks with Markovian jumping parameters can be included as a special case of our main results. Finally, numerical examples are given to illustrate the applicability of the proposed design method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grants GR/S27658/01, an International Joint Project sponsored by the Royal Society of the UK, the National Natural Science Foundation of China under Grants 60774073 and 60804028, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, and the Alexander von Humboldt Foundation of Germany

Robust tool wear monitoring using radial basis function neural networks

A robust monitoring scheme for tool wear is presented in this thesis. The nonlinear nature of most dynamic problems makes modeling and subsequent analysis difficult. A generic method for approximation of nonlinear systems is considered in this thesis. Radial basis functions provide a means to learn and model nonlinear systems based on a few sample runs. This property is used to develop models from experimental data. Subsequent usage of the models requires that a state estimation scheme be developed. An upperbound covariance method is presented to minimize divergence problems arising from modeling inaccuracies. Example applications of this method are presented in this thesis. A complete study of the use of these basis functions for representing tool wear evolution is investigated. Using prior experimental data, the basis functions are trained for subsequent use in monitoring. The effect of flank and crater wear on the cutting forces has been analytically modeled to minimize the number of experiments performed. The effect of flank wear on the indentation process has been studied to model force-wear relationships. The influence of crater wear on shear plane angle has been investigated to aid in prediction of force changes with crater wear. Predictions of forces for tools with flank wear has been shown to be more accurate than the crater wear case. By making use of the analytically determined output equations, a robust tool wear monitoring scheme has been implemented. Experimental results using carbide and ceramic inserts are considered. The estimation of flank wear is seen to be reasonably good, while crater wear estimates remain poor