Research On State Boundedness Of Memristive Neural Networks

Artificial neural networks play an important role in the development of artificial intelligence technology,and at present,the research on artificial neural networks has achieved very fruitful results.The appearance of the memristor provides a new idea for the realization of neural network operations,and the concept of memristive neural network came into being.The mathematical expression of the memristive neural network is a kind of switching system.Therefore,many concepts in the classical control theory have been introduced into the memristive neural network analysis method.The state boundedness is a basic concept in the control theory,and it is very important to get the possible range of the system state,for example,the state exceeds a certain range may cause the system to fail to operate safely.Therefore,state boundedness is a prerequisite for the successful application of memristive neural networks in practice,there are related documents published as early as 1960.In practical applications,such as safety verification and aircraft collision avoidance,designing controllers,etc.,there are many applications in these areas,and the state boundedness of memristive neural networks has naturally become an important research content.First of all,Chapter 2 derives the estimation of the reachable set of complex-valued memristive neural networks.For the study of memristive neural networks,compression maps are usually constructed,then using differential inclusion and set-valued mapping theories to study its dynamic behavior under the framework of Filippov solutions.And using two different methods,linear matrix inequality and algebraic methods,to solve complex-valued memristive neural network solution's boundary range,in which the linear matrix inequality method transforms the reachable set problem into an optimization problem,and gives the sufficient condition of the minimum ellipsoidal domain containing the reachable set of the system solution,the algebraic method uses inequality technology to obtain the boundary of the system solution.Secondly,due to the fuzzy concepts in human brain thinking,Takagi introduced a kind of fuzzy logic used in 1985 and has been widely used afterwards,and its combination with neural networks can establish a symbiotic complementary system.Chapter3 research a class of fuzzy memristive neural network state bounded problems.By introducing the definitions of Metzler matrix and Hurwitz matrix,using the comparison theorem of functional differential equations,a sufficient condition for the state boundedness of fuzzy memristive neural networks is obtained,and an improved method is also given on this basis.Again,in Chapter 4,it is considered that the process of neurotransmitter transmission will inevitably be interfered by the external environment.To study the dynamic behavior of memristive neural networks more accurately,the influence of random noise must be considered.For the same reason,the use of neural networks to simulate neurons will also be subject to various disturbances.By introducing the M matrix and differential inequality into Lyapunov's theory,we give the criterion for judging the asymptotic boundedness and almost surely stability of stochastic memristive neural network.Finally,for different research contents in Chapter 2-4,we give numerical examples to prove the validity of the results.This research topic enriches the related results of the research on the state of memristive neural network,and provides theoretical support for the application of memristive neural network in artificial intelligence.