Analysis And Control Of Memristor Neural Networks With Unbounded Time-varying Dela

As one of the hottest research areas today,neural networks have attracted significant research interests from both industry and academia,and have also had a significant social impact.Neural networks have shown great potentials in various applications such as associative memory,secure communication,visual recognition,medically assisted detection and so on.As the fourth basic element of the circuit:the memristor has many advantages such as small size,speed,low energy consumption,high integration and non-volatility.More importantly,the analog function of memristors in circuit elements enables synapses among neurons to be realized in a highly efficient manner,the memristor is considered to be the most promising class of components for simulating human brains.Therefore,we can use memristors to build a new artificial neural network model,namely,memristor-based neural networks.It is well known that time delays,especially time-varying time delays,inevitably arise due to information exchange and signal transmission among neurons.Moreover,the current state of neurons is affected by all its historical information,so the time delay should be considered unbounded,which can more realistically mimic the behavior of neurons in the human brain.Therefore,researching memristor-based neural networks with unbounded time-varying delays are very valuable in theory and practice.In this thesis,we focus on the global exponential stabilization,the Lagrangian exponential stability and stabilization,the bounded real lemma and exponential H∞control,and the observer-based H control of memristor-based neural networks with unbounded time delays.The main research contents are as follows:Firstly,the problem of global exponential stabilization of memristor-based neural networks with unbounded time-varying delays is investigated.Without transforming the model or constructing any Lyapunov-Krasovskii(L-K)functional,the global exponential stabilization criterion of memristor-based neural networks with unbounded time-varying delays is derived directly from the definition of global exponential stability.The superiority of this method is verified by three numerical examples.Secondly,exponential Lagrangian stability and stabilization problems for memristor-based neural networks with unbounded time-varying delays are investigated.Again,without transforming the model or constructing any L-K functional,the exponential Lagrangian stability criterion for the memristor-based neural networks with unbounded time-varying delays is given,and the exponential Lagrangian stabilization criterion is given based on the obtained stability criterion.The validity of the method is verified by two numerical examples.Then,we study the bounded real lemma and exponential H∞ control problem for memristor-based neural networks with unbounded time-varying delays based on the definition.We directly derive sufficient condition guarantee the global exponential stability of the system,and a prescribed H∞ performance level(i.e.,bounded real lemma).And then the exponential H∞ controller is designed based on the obtained bounded real lemmas.The applicability of the method is verified by two numerical examples.Finally,the observer-based H∞ control problem for memristor-based neural networks with unbounded time-varying delays is investigated.An appropriate observerbased controller is constructed to ensure not only the global exponential stability of the undisturbed augmented dynamical system,but also the H∞ performance level of the original system.The validity of the method are verified by two simulation examples.The novelties of this thesis are summarized as follows:(1)no model transformation is required;(2)the construction of L-K functionals is avoided;(3)the obtained sufficient conditions are easy to solve;(4)the proposed method can be extended to many neural network models.