Modeling And Control Of Memristive Circuit Systems

The implementation of memristor provides a novel way to design circuits and achieve new functions. The non-volatile property of memristor provides a good chance to meet the challenges in front of Neuromorphic Computation. And memristor is a promising solution for learning and training of Artificial Neural Networks. Along with the development of Artificial Neural Networks, the memristor will play a key role in the fuzzy logic, genetic algorithm and neuro-fuzzy systems. Therefore, modeling and control of memristor-based complex system becomes the focus of memristor research.Otherwise, the complex the dynamical behaviors of systems become will make it diffi-cult to recognize the pattern of the model in time serize, therefore, it is urgent to employ the reconstruction of the data attractors. This is the cause why people plug into the discovery of chaotic systems. However, as the state-dependence of memristor, there are few works on the research of synchronization of memristor-based chaotic systems.Meanwhile, it is necessary to investigate the passive problem for circuit systems to guarantee the inter stability of the whole system. And there exist noise disturbances and variable time-delays in the memristor-based circuits. Therefore, it is necessary to investigate the noise disturbances in the process to study the passivity problem of memristor-based delayed piecewise linear systems. However, there are no related works on the passivity problem of stochastic impulsive system with mixed delays.The terminal implementation of memristor will be in artificial intelligent as Artificial Neural Networks at last. However, the problems about the circuit design and system model-ing of memristor-based recurrent neural networks as well as related delay-dependent expo-nential passivity and global exponential synchronization are open for further discovery.As the memristive systems become intelligent, it is necessary to investigate the coop-eration problem of memristor-based intelligent systems and design corresponding protocols to solve the problems of existing delays and data losses in the communication networks between the control systems or other applications. Then how to reduce the communication between the sensors and control nodes evokes researchers great interesting.Based on the above discussion, Lyapunov stability theory, matrix theory, inequality, fuzzy method are employed to investigate the modeling and control of memristive circuit systems. The main contents and inventions include:New memristor-based circuit systems, as well as corresponding dynamical equations are set up. Then, we investigate the synchronization problem between circuits with differ- ent parameters, as well as different circuits, and study the passivity problem of memristor-based stochastic piecewise systems with mixed delays. A controller is designed by a new Lyapunov-Krasovskii functional to make the closed system global passive. The gains of the controller can be obtained by the related LMIs. And the obtained results can be extended to general systems.And the delay-dependent exponential passivity problem of memristor-based recurrent neural networks has been discussed with the information of the neural activation functiona and varying-time delays. Compared with existing references, the obtained results reduce computational burdens and conservativeness. Furthermore, we design a new memristor-based recurrent neural networks, set up correponding dynamical equation, employ PDC fuzzy strategy to study these networks, and investigate the global exponential synchroniza-tion problem of these networks. Furthermore, we compare the obtained results with existing ones.Then, we study the distributed event-triggered control of memristive systems. First, a new PDC fuzzy method is employed to linearize the complex memristive systems into two subsystems, then, an event-triggered control strategy is taken to update the controller to stabilize the memristive systems, and the obtained results are extended to the systems with quantization and network induced delays, and the controller is updated only at its own event times, this will reduce the communication and the update frequency of the controller.All these works deeply discovery the properties of memristor-based circuit system, which will promot the study of memristor, and provide reliable clues for the implementation and application of memristor-based circuits.