Synchronization Control Of Neural Networks With Fractional-order

Since the 21st century,as a promotion of classical calculus,fractional calculus has been widely used in many fields such as complex viscoelastic materials,system control,biomedical engineering,high-energy physics,and economics,which has fuelled a research boom at home and abroad.Owing to the unique features of nonlocality,memory and heredity of fractional calculus,it has important practical significance and research values to describe the characteristics of neurons' cognition,decision-making and adaptation by introducing the fractional calculus into neural networks.Therefore,in this thesis,some useful theories,including fractional calculus,the theories of neural networks and complex-variable functions,system control theory,will be comprehensively utilized to deeply carry out analysis and discussion on synchronization control of several types of fractional-order neural networks.Without separating complex-valued neural networks into two real-valued systems,the finite-time synchronization is addressed for a class of fully complex-valued neural networks with fractional-order in the first part.First of all,a fractional-order differential inequality is established on the complex domain,then the sign function of complex numbers is proposed and some properties about it are derived.Based on the proposed sign function framework,two power-law feedback control schemes are respectively designed under different norms.Additionally,by constructing nontrivial Lyapunov functions and using the new fractional-order differential inequality,several criteria of finite-time synchronization are derived and the settling-time of synchronization is effectively estimated.In the end,the theoretical results are verified by some numerical examples.Considering the influence of time delay and reaction diffusion on the neural networks,the problem of Mittag-Leffler synchronization for a class of fractional-order reactiondiffusion neural networks with Dirichlet boundary conditions is discussed in the second part of the thesis.Firstly,based on the L'H ?opital law,a Caputo fractional partial differential inequality with p-norm is established to improve the previous results.Furthermore,the centralized control scheme and distributed control scheme are designed for the networks,respectively,then the criteria of Mittag-Leffler synchronization are obtained by using the inequality technique and the property of Mittag-Leffler function.Finally,numerical examples and simulations are provided to verify the correctness of the results.Directly based on the synchronization error method,we investigate the problem of fractional-order adaptive synchronization of coupled complex-valued networks with fractional-order in the third part.Firstly,the fractional-order adaptive strategy is designed for the complex-valued coupling weight,the new Lyapunov function is constructed by defining the state error between any two nodes,and the asymptotic synchronization criterion for coupled complex-valued networks is established by using the complex variable function theory.In addition,based on the connected dominating set,the fractional-order adaptive pinning protocol is developed which only depends on the information of subgraph composed of the connected dominating set with their neighbours.Finally,two numerical examples are given to verify the effectiveness of the adaptive strategies.