The Research On State Estimation And Reachable Set For Memristive Neural Networks

In the development of artificial intelligence,Neural Networks have played an important role,and the emergence of memristors has further advanced the computation of Neural Networks,leading to the development of Memristive Neural Networks(MNNs).Mathematically,MNN is right-discontinuous switched system.It is a stochastic process system,and the state jumps occur with the change of state,that is,it is a state-dependent switched system.Thus,many concepts in control theory have been introduced into the analysis of MNNs,and state estimation is one of the important concepts in control theory,from which reachable sets are derived.Due to technological limitations,it is difficult to obtain the state information of MNNs.Moreover,due to limited signal transmission and switching speeds,MNNs usually have various types of time delays,which can lead to poor performance of the system,including instability and oscillation.Therefore,state estimation and reachable set estimation have become important research topics.Firstly,Chapter 2 derives the problem of state estimation for MNNs.In general,research on MNNs usually uses differential inclusions and set-valued mapping theory to study the dynamic behavior of solutions in the Filippov sense.When studying state estimation problem,it is necessary to construct a state observer and error system.Based on Lyapunov-Krasovskii functions(LKF),linear matrix inequalities(LMI),free weighting matrix methods,and some inequalities,sufficient conditions for delay-independent and delay-dependent asymptotic stability of the error system are investigated.Secondly,due to the presence of bounded disturbances in the system,Chapter 3 investigates the problem of state estimation and reachable set for MNNs with bounded disturbances.A state observer with Bernoulli sequences is designed,and sufficient conditions for global mean square stability of the error system are obtained.Furthermore,using algebraic conditions,the reachable set of the MNNs is obtained,and ellipsoid and ball domains containing all the state information are derived under zero and nonzero initial conditions,respectively.Thirdly,in Chapter 4,considering that the process of neurotransmitter transmission in the human brain is inevitably subject to external interference,the influence of random noise should be taken into account to more accurately study the dynamic behavior of MNNs.Similarly,using Neural Networks to simulate neurons will also be subject to random interference.By utilizing the Ito formula and LMI,conditions for state estimation and reachable set estimation of random MNNs are obtained.Finally,simulation examples are presented to demonstrate the validity of the conclusions for the different research topics in Chapters 2-4.This research enriches the related results of state estimation and reachable set estimation for MNNs and provides theoretical support for the application of MNNs in artificial intelligence.