The Study On Finite-time Synchronization Of Memristive Neural Networks

Biological neural network(BNN)is a network model composed of a large number of neurons interconnected with other neurons through synapses.Artificial neural network(neural network)is modeled after BNN’s characteristics.Memristor is the best circuit element used to simulate synapses at present.Memristive neural network(MNN)is a kind of model which is obtained by replacing ordinary resistors with memristors.Therefore,MNN model is closer to the structure of human brain.Both integer-order and fractional-order MNN researches have attracted the attention of scholars.Different from asymptotic synchronization,finite-time synchronization can realize synchronization of networks within a setting time.The theory of finite-time synchronization can guide the selection of control parameters and realize synchronization within the expected time,which has more practical application significance.In addition,from the perspective of social production,people often hope to solve practical problems by using the least control resources.Therefore,how to select the optimal control parameters becomes an important problem to be solved.In conclusion,this thesis mainly studies the finite-time synchronization of MNN.Then one optimizes the control parameters and obtains the optimal control parameters of controllers.The performance of all the theories and methods proposed in this paper is verified by numerical simulations.The specific works of the thesis are as follows:Firstly,one studies finite-time synchronization and fixed-time synchronization of inertial MNNs with proportional delays and switching jump mismatch.By introducing a new variable,the second-order inertial MNN model is transformed into a mathematical model consisting of two first-order differential equations.Two appropriate controllers are designed respectively to obtain the conditions of finite-time synchronization and fixed-time synchronization,and the setting times are obtained concurrently.Then,an optimization method of selecting the optimal control parameters is proposed by establishing an optimization model of control parameters and giving the specific steps of solving the model combined with particle swarm optimization algorithm,so as to receive the optimal control parameters.Secondly,one studies finite-time bipartite synchronization of coupled MNNs with multiple time delays and signed graph.There are both cooperative and competitive relationships between neurons in the network.A controller with sign function is designed to obtain conditions of finite-time bipartite synchronization.A controller with saturation function is designed to avoid chattering phenomenon caused by sign function,and one can obtain conditions and setting time of practical finite-time bipartite synchronization.Based on these,fixed-time and practical fixed-time bipartite synchronization are discussed as well.Then,an optimization method of selecting optimal control parameters is proposed.Thirdly,one studies finite-time multiparty synchronization of T-S fuzzy coupled MNNs with a time delay.The mathematical models are presented respectively,which include coupled MNNs and a leader by fuzzy mixing based on fuzzy rules.An eventtriggered controller is designed to obtain the conditions for realizing finite-time multiparty synchronization of the networks.The Zeno phenomenon that may occur in the event-triggered controller is excluded.In addition,the optimal control parameters are obtained by using the optimization method of control parameters.Then,one compares the optimal parameters with a novel event-triggered controller designed in another paper.Fourthly,one studies finite-time projective synchronization of structure-dependent fractional-order MNNs with a time delay.Fractional-order network model is an extension of integer-order network model,which can better simulate the practical model.In structure-dependent MNNs,the corresponding memristor coefficients are different even if the states of drive-response networks are the same.A suitable controller is designed to obtain conditions and setting time for achieving finite-time projective synchronization of networks along with fractional stability theory.Then,the optimal control parameters are obtained by optimization design of control parameters.The study results of different projective coefficients are verified by simulation.Finally,one studies finite-time cluster synchronization of fractional-order complexvalued coupled MNNs.Neurons in different clusters follow different leaders to achieve finite-time synchronization.Instead of decomposing the complex-valued network into two real-valued networks,a controller with complex-valued sign function is designed.Conditions and the corresponding setting time of finite-time cluster synchronization are obtained by non-decomposition method.Then,the optimal control parameters are gained by using the control parameters optimization method.And the optimal controller is compared with a controller proposed in another paper.