Finite-time Synchronization Control And Applications Of Fractional-order Memristive Neural Networks

With the further improvement of urbanization in China,the supply-demand relationship between urban traffic demand and traffic resources is out of balance.As a result,traffic congestion is becoming increasingly acute in metropolitan areas.Moreover,traffic congestion would gradually spread along the urban traffic network.If a single point of traffic congestion can’t be solved properly,it will cause a wider range of traffic congestion and even paralysis.The way how to alleviate urban traffic congestion quickly and effectively,has become one of the most important topics in the field of modern intelligent transportation.In recent years,along with rapid development of artificial intelligence technology,neural network synchronous control strategy has been applied to the control system of urban traffic network,which has a great effect on improving the traffic efficiency of urban traffic network and alleviating traffic congestion.Memristor is a kind of non-linear resistor with memory function.Because of the small size,low energy consumption and easy integration,memristor is considered to be the prefect device for simulating synapse.From the mathematical point of view,fractional calculus can accumulate the global information of the function in the weighted form,which are more accurate one in describing the memorability and heredity of neurons.As mentioned above,memristor and fractional-order calculus have been incorporated in to artificial neural networks for describing the dynamic behavior of neurons suitably and improving the ability of parallel computing and adaptive learning.For one thing,with the help of feedback and periodically intermittent controller,this thesis discusses the finite-time synchronization of fractional system.For another,in order to improve the run efficiency of urban traffic network,the theorem of finite-time synchronization has been applied to regional perimeter control system,which provides a novel control idea for improving the efficiency of traffic network and alleviating urban traffic congestion.Finally,the main work of this thesis is as follows:(1)Under the framework of Filippov sense,this thesis is concerned with the problem of synchronization for fractional-order Cohen-Grossberg memristive neural networks and fractional-order Hopfield memristive neural networks with feedback and periodically intermittent controller.And some sufficient criteria have been established to ensure the finitetime synchronization.Besides,according to the asymptotic expansion property of MittagLeffler function and Gronwall inequality,a novel synchronous control method is proposed,and the obtained synchronous control condition is more accurate and less conservative.(2)For the methods of constructing Lyapunov functions,we also consider a more flexible p-norm form of synchronization error function besides the frequently-used 1-norm form.With the help of fractional derivation rule for power functions,Young inequality and Jensen inequality,the convergence theorem of fractional order differential inequality in Lp-norm form is obtained.(3)Based on the Macroscopic Fundamental Diagram(MFD),a fractional-order state-space equation of two urban regional road networks perimeter control system is constructed.Further,the results of finite-time synchronous control are applied in two urban regional road networks perimeter control system.And under the feedback and periodically intermittent controller,some sufficient synchronization criterion between the control system and target and estimation expressions of synchronization time are obtained.