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Dynamic Analysis Of Neural Networks With Discontinuous Righthand

Posted on:2015-05-05Degree:DoctorType:Dissertation
Country:ChinaCandidate:J XiaoFull Text:PDF
GTID:1228330428984304Subject:Systems analysis and integration
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As we know, one system can be represented by continuous differential equations; but, in practical applications, many science problems can not be modeled and solved by continu-ous differential equations. In numerous methods, it is a good choice employing differential equations with discontinuous righthand to reveal the nature of problems. For systems with discontinuous righthand, there are two sources which can bring in the discontinuity. On the one hand, there exist discontinuities in systems themselves because of different reasons. On the other hand, in control design, there exist some classes of systems which can be made realize our expected performances by continuous control laws, but it can be achieved by discontinuous control laws; what is more, discontinuous control law have some advantages that continuous control laws are without. So it is an interesting work to study the theories and applications of systems with discontinuous righthand.Neural network is a class of nonlinear system having special features. And, neural networks have achieved many successful applications in different fields for example pattern recognition, optimization, associative memory and so on. Until now, most published litera-tures are referring to continuous neural networks. However, as far as we know, there exist a great deal of neural networks with discontinuous righthand in practical applications. For example, famous M-P neural networks are with discontinuous activation functions. Hence, it is necessary to investigate neural networks with discontinuous righthand, it is beneficial for designing useful neural networks.Considering the above discussion, this dissertation will study neural networks with discontinuous righthand from two different aspects:neural networks with discontinuous activation functions and memristor neural networks with discontinuous parameters. Since the definitions of solutions for differential equations in conventional sense can be employed for systems with discontinuous righthand, based on the definitions of solutions in Filippov sense, we discuss the dynamical behaviors by means of linear matrix inequalities (LMI), matrix analysis method, Lyapunov function method, nonsmooth analysis approach and so on. The corresponding contents and innovations are listed as follows.To our knowledge, the dynamic behaviors of neural networks not only depend on the their parameters but also rely on their activation functions. So it is beneficial for designing neural networks to select a general class of activation functions. Moreover, most of exist-ing results with respect to discontinuous neural network are based on the assumption that the activation functions are monotone-nondecreasing or bounded, so we investigate global asymptotical stability of a general class of neural networks, where discontinuous activa-tion functions are not restricted to be monotone-nondecreasing or bounded. The sufficient conditions for global asymptotical stability are presented by means of LMI method and dif-ferential inclusion theory. The results are useful supplements for neural networks’research.Passivity can guarantee the internal stability of systems, it reveals the relationship be-tween inputs and outputs and is an important tool for designing systems. So far, to our knowledge, there are no related works on the neural networks with discontinuous activation functions. Therefore, we discuss the passivity of neural networks. The corresponding cri-teria for passivity are established by employing nonsmooth analysis theory. And, based on passivity, the stabilization control law is given out to ensure neural network be asymptoti-cally stable.State observer is an important tool to estimate the states of systems by using mea-surement outputs. In published literatures, measurement outputs is usually assumed to be smooth, there are few works on the state estimation of discontinuous neural networks. Thus, we consider a general class of neural networks, where discontinuous activations are linear growth but not monotone-nondecreasing, and measurement outputs are locally Lipschitz but not smooth. By using of LMI and nonsmooth analysis theory, the corresponding designs of state observers are proposed for certain neural networks and uncertain neural networks, re-spectively. The state estimation gain can be achieved by solving corresponding LMI, so the designing approaches can be easily realized.Input-to-state stability is an important aspect of stability analysis, which is different from the stability in Lyapunov sense in nonlinear systems. Thus, we study the input-to-state stability of neural networks with discontinuous activations using matrix analysis theory, LMI and nonsmooth analysis theory. And the corresponding M-matrix criterion and LMI criterion are established.Memristor is a fourth basic circuit element besides resistor, capacitor and inductor. The value of resistance of memeristor can changing with electric current (voltage). Memristor has many useful feature for example memorability. Influenced by memristor’s features, cor-responding novel memristor neural networks are a class of systems, whose parameters are discontinuous and changing with the states of systems. Therefore, memristor neural net-works have more complicated nonlinear behaviors. Thus, we research the global asymptot-ical stability and stabilization control of memristor neural networks employing nonsmooth analysis theory. Using differential inclusion theory and matrix analysis approach, the suf-ficient conditions are presented to ensure neural networks globally asymptotically stable, then, stabilization control laws are established while inputs are not constant.The given results are beneficial for revealing the nature of neural networks. They can enrich the theory of neural network and guide the applications of neural networks, so the given results are useful.
Keywords/Search Tags:Neural network, Discontinuous righthand, Differential inclusion, Asymptoticalstability, Passivity, State estimation, Input-to-state stability, Memristor, Mem-ristor neural network
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