Research Of Adaptive Synchronjzation For Nonlinearly Parameterized Complex Dynamical Network

In the past ten years, complex dynamical network and its research were widelyused in many fields, such as social economy, biological engineering, mechanicalengineering, etc. Nonlinear dynamics of complex dynamical network and the topologyof the network affect its dynamic behavior, and the research of synchronization ofcomplex dynamical network has become a challenging and hot issue. It has veryimportant significance for understanding the behavior of the group cooperationmechanism and laws, and the complex phenomenon in nature and society to researchthe synchronization of network. It has a very broad application prospect in the nuclearmagnetic resonance, wireless sensor network and multi-robot coordination.Considering dynamical network in reality has nonlinear coupling and existence oftime-varying parameter increases the difficulty of study about complex dynamicalnetwork, this paper puts forward a kind of adaptive learning control method. By usingthe parameter separation and re-parameterization technology, the adaptivesynchronization of nonlinearly coupled system with unknown time-varying parametersis studied. Through putting forward the periodic time-varying parameter and constantparameter adaptive learning law, the adaptive control law guarantees synchronizationerror to converge to zero inL_T~2norm sense.Motivated by the above discussions, this paper mainly includes the followingaspects:Firstly, for a class of nonlinearly parameterized complex dynamical network withunknown time-varying parameters, we put forward a kind of adaptive learning controlmethod to make the adaptive synchronization of complex dynamical network to anygiven state. The convergence of synchronization error is proved by constructingcombined energy function and using the method of Lyapunov theory. A simulationexample shows the validity of this method.Secondly, considering hybrid functional projective synchronization of complexdynamical network is widely used in secure communication and information security,use the adaptive learning control and the Lyapunov theory to prove hybrid functionalprojective synchronization of nonlinearly coupled complex dynamical network withunknown time-varying parameter.At last, consider average consensus of complex dynamical network with nonidentical nodes. This network has unknown time-varying nonlinear coupling term.Using separation principle and the adaptive learning control method, make thecomplex dynamical network synchronize to average of system state. Finally, thesimulation example verifies the feasibility and validity of the method.