On Synchronization Control Of Discontinuous Complex-valued Neural Networks

With the rise of artificial intelligence,artificial neural networks have become a re-search hotspot and have been developed rapidly since the 1980s.Complex-valued neural networks,as an important class of artificial neural systems,have stronger information s-torage capabilities than real-valued neurons,and can solve many complex problems which cannot be solved by real-valued neural systems.In view of the extensive applications,as a theoretical basis,the dynamic characteristics and synchronization control of complex-valued neural networks have been thoroughly discussed in recent years.However,most of the current results mainly focus on asymptotic synchronization by separate the complex-valued networks into two real-valued subsystems.Contrarily,the theoretical analysis for finite-time synchronization and fixed-time synchronization has not caused much attention although they have more practical significance.Based on the above discussion,by com-prehensively applying the complex-variable function theory,nonsmooth analysis tech-niques,differential equations with discontinuous right-hand sides,impulsive differential equations and other related theories,this thesis will investigates finite-time and fixed-time synchronization of complex-valued neural networks with discontinuous activation func-tions,fixed-time synchronization of coupled memristive complex-valued neural networks and global asymptotic synchronization of impulsive coupled complex-valued neural net-works respectively.First of all,the finite-time and fixed-time synchronization of complex-valued neural networks with time delays and discontinuous activation functions is researched.Unlike the previous separation technique used for complex-valued networks,the sign function is introduced into the complex field to design a discontinuous controller for the control complex-valued systems.Meanwhile,by extending the traditional measurable selection theory to the complex domain,the finite-time synchronization criteria of complex-valued neural networks are obtained.Furthermore,in the sense of the absolute value norm,an interesting conclusion can be obtained by designing a unified control strategy,that is,the key parameter value in the unified control strategy completely determines whether the master-slave systems ultimately is finite-time synchronization or fixed-time synchroniza-tion.Finally,a numerical example is given to verify the establishment theoretical results.Memristor is introduced into complex-valued neural networks in the second part of this thesis and the fixed-time synchronization for a class of coupled memristive complex-valued neural networks is investigated.Firstly,a new fixed-time stability theorem is es-tablished to weaken the existing conditions of fixed-time stability and improve the estima-tion of the settling time.Additionally,by removing the linear part,some complex-valued power-law control schemes are designed to simplify the traditional control designs,which are composed of linear part to ensure the asymptotic synchronization and power-law con-trol to ensure the fixed-time synchronization.Moreover,by using the theory of complex functions and the established theorem of fixed-time stability,the criteria of fixed-time synchronization and the estimate for the settling time are obtained.Finally,the feasibility of theorems and control strategies is verified through a given numerical example.Different from the previous continuous communication and fixed topology,the third part of this thesis proposes a discontinuous communication mechanism where network-s'nodes only exchange information at some discrete times,and the global asymptot-ic synchronization for a class of impulsive coupled complex-valued neural networks is discussed based on the sequence connection structure.First,motivated by the idea of se-quence connectivity,a coupling strategy with switching disconnected topology and impul-sive communication pattern is proposed.Secondly,by applying the direct error method,convex combination and the way of iteration,the synchronization conditions are estab-lished for complex-valued neural networks with impulsive coupling.In order to illustrate the correctness of the theoretical results,relevant numerical simulation is finally provided.