The Control And Applications Of Stochastic And Switched Dynamical Complex Networks

In recent years, complex networks have received a great deal of attentionof the researchers from diferent fields, such as mathematics, physics, computerscience, biology, economics and social science etc. The control and optimizationof the complex dynamical networks has been one of the most important topicsof complex networks. In this dissertation, we investigate the control problemsof the complex networks system with stochastic and switched dynamics, and thecoordinated control problems of complex multi-agent networks and the complexsupply networks. The main contents and innovative points are presented asfollows:A method of the guaranteed cost control of synchronization for the complexdelayed network with stochastic disturbance is proposed. By the guaranteed costcontrol technique, the guaranteed cost control of synchronization for uncertainstochastic complex networks with time-varying delays is studied. By designingthe guaranteed cost controller, sufcient condition for the mean square synchro-nization of uncertain stochastic complex delays networks is given. Moreover,sufcient condition for the existence of the optimal guaranteed cost control lawsis given.A method of the robust H_∞control for the impulsive switched complex de-layed network is proposed. Sufcient condition is developed to ensure robustlyglobal stability and a prescribed H_∞disturbance attenuation level for the result-ing closed-loop networks in terms of linear matrix inequalities (LMIs). A convexoptimization problem is formulated to determine the optimal state feedback H_∞controller which guarantees the optimal H_∞disturbance attenuation level.A method of the H_∞control for the synchronization of the singular complexdelayed network with stochastic switched coupling is proposed. The switchedcoupling is dependent on a continuous time Markov process. Sufcient conditionsfor the existence of the H_∞control laws are given in terms of linear matrixinequalities, which ensure robustly global mean square synchronization and a prescribed H_∞disturbance attenuation level for the resulting closed-loop complexnetworks.A method of the impulsive consensus control of noise perturbed multi-agentsfollowing leader with stochastic switching topology is proposed. Sufcient condi-tion is given to guarantee the mean square consensus of all the agents followingthe virtual leader by designing the impulsive protocol for each agent.The adaptive flocking control of multi-agents following leader with commu-nication delays in noise environment is proposed. By introducing the adaptiveprotocol compensating for the desired velocity, a new neighbor-based flockingprotocol is proposed such that all the agents move with a virtual leader’s veloc-ity, and avoidance of collision between the agents is ensured.A complex supply network with stochastic switching topology and the un-certain demand is presented, in which the switched coupling is dependent on acontinuous time Markov process. By the robust H_∞control method, the robuststabilization strategy is designed for the complex supply network with stochasticswitching topology, which ensure a prescribed H_∞disturbance attenuation forthe uncertain demand, and improve the coordination and the robustness of thewhole supply network.