忆阻电路系统的建模与控制
摘要
忆阻器的成功研制为电子电路的设计提供了新的途径并使该电路具有新的功能.其非易失性可以更好地解决神经计算中所面临的问题和挑战.忆阻器将会在人工神经网络的学习和训练中起到非常重要的作用,而随着人工神经网络的发展,忆阻器也将会在模糊逻辑,基因计算、和神经-模糊系统中起关键作用.因此,基于忆阻器的复杂系统的建模和控制问题成为了忆阻器研究的重点和前沿.
另外,当系统的动态行为变得复杂的时候,就会使得对此时间序列中重复或接近重复的模式的识别变得比较困难,因此使用数据吸引子的重构变得尤为重要.这也是人们为何迫切要去发现混沌系统的原因.然而由于忆阻器的状态依赖性,目前对于基于忆阻器的混沌系统的同步控制相关的研究成果还比较少.
同时为了从本质上保证整个电路系统的内部稳定性,需要考虑它的无源性问题.在实际基于忆阻器的电路中不可避免存在着噪声扰动和各种时滞.而目前还没有见到关于带混合时滞的随机脉冲系统的无源性研究的相关工作的报道.
忆阻器最终的用途之一是实现人工智能而广泛应用于人类脑神经网络.但目前为止,基于忆阻器的递归神经网络的电路设计与系统建模,以及相关系统的时滞依赖指数无源性和全局指数同步问题都还是公开问题,值得人们进行深入研究.
随着忆阻系统的智能化,人们需要对基于忆阻器的智能系统的协调控制进行研究,建立相应的协议以解决控制系统或其他应用之间存在的通讯网络时滞和信息丢失问题.在实际中,往往会遇到在极短的传输时间需要传输大量数据的问题,怎样减少传感器和控制极点之间的通讯已引起人们极大的兴趣.
基于上述考虑,本文利用Lyapunov稳定性理论、矩阵理论、不等式、模糊化方法等分析工具对忆阻电路系统的建模和控制进行深入系统的研究.研究内容及创新成果包含以下几个方面：
建立了新的基于忆阻器的电路系统,得到了相应的动力学方程,研究了带有不同参数的基于忆阻器的电路系统的同步问题,以及基于忆阻器的不同电路系统的同步问题.
研究了一类基于忆阻器的带混合时滞的随机脉冲分段线性系统的无源性问题.采用一个新的Lyapunov-Krasovskii函数来设计控制器,使得闭环系统是全局无源的.控制器的参数可以通过求解相关的线性矩阵不等式(LMI)获得.所得结果也可应用于一般系统.
讨论了基于忆阻器的递归神经网络的时滞依赖指数无源性问题.在这个过程中,充分考虑了神经元激励函数和时变时滞的信息,与已有相关文献相比,减少了计算量和保守性.同时分析和研究了基于忆阻器的递归神经网络的全局指数同步问题,设计了一种新的基于忆阻器的神经网络,建立了相应的动态方程,并采用并行分布式补偿(PDC)模糊策略来分析此系统,并将所得结论与已有结果进行了比较.
研究了带事件触发控制器的忆阻系统的分布式控制问题,采用一种新的PDC模糊化方法将复杂的忆阻系统线性化为两个子系统,提出了一种事件触发控制策略来更新控制算法从而镇定忆阻系统,并将所得结果扩展到带量化和网络时滞的系统,控制器只在自身触发时更新,这样就减少了通讯量并降低了控制器的更新频率.
这些研究工作深刻揭示了基于忆阻器的电路系统的本质特征.既丰富了忆阻器研究的理论成果,又为基于忆阻器的电路实现与应用技术提供了可靠的依据,具有非常重要的应用价值.
The implementation of memristor provides a novel way to design circuits and achievenew functions. The non-volatile property of memristor provides a good chance to meet thechallenges in front of Neuromorphic Computation. And memristor is a promising solutionfor learning and training of Artificial Neural Networks. Along with the development ofArtificial Neural Networks, the memristor will play a key role in the fuzzy logic, geneticalgorithm and neuro-fuzzy systems. Therefore, modeling and control of memristor-basedcomplex 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 thereconstruction of the data attractors. This is the cause why people plug into the discoveryof chaotic systems. However, as the state-dependence of memristor, there are few works onthe research of synchronization of memristor-based chaotic systems.
Meanwhile, it is necessary to investigate the passive problem for circuit systems toguarantee the inter stability of the whole system. And there exist noise disturbances andvariable time-delays in the memristor-based circuits. Therefore, it is necessary to investigatethe noise disturbances in the process to study the passivity problem of memristor-baseddelayed piecewise linear systems. However, there are no related works on the passivityproblem of stochastic impulsive system with mixed delays.
The terminal implementation of memristor will be in artificial intelligent as ArtificialNeural 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 protocolsto solve the problems of existing delays and data losses in the communication networksbetween the control systems or other applications. Then how to reduce the communicationbetween 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 circuitsystems. The main contents and inventions include:
New memristor-based circuit systems, as well as corresponding dynamical equationsare 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 newLyapunov-Krasovskii functional to make the closed system global passive. The gains of thecontroller can be obtained by the related LMIs. And the obtained results can be extended togeneral systems.
And the delay-dependent exponential passivity problem of memristor-based recurrentneural networks has been discussed with the information of the neural activation functionaand varying-time delays. Compared with existing references, the obtained results reducecomputational burdens and conservativeness. Furthermore, we design a new memristor-based recurrent neural networks, set up correponding dynamical equation, employ PDCfuzzy strategy to study these networks, and investigate the global exponential synchroniza-tion problem of these networks. Furthermore, we compare the obtained results with existingones.
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 intotwo subsystems, then, an event-triggered control strategy is taken to update the controller tostabilize the memristive systems, and the obtained results are extended to the systems withquantization and network induced delays, and the controller is updated only at its own eventtimes, 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 implementationand application of memristor-based circuits.
另外,当系统的动态行为变得复杂的时候,就会使得对此时间序列中重复或接近重复的模式的识别变得比较困难,因此使用数据吸引子的重构变得尤为重要.这也是人们为何迫切要去发现混沌系统的原因.然而由于忆阻器的状态依赖性,目前对于基于忆阻器的混沌系统的同步控制相关的研究成果还比较少.
同时为了从本质上保证整个电路系统的内部稳定性,需要考虑它的无源性问题.在实际基于忆阻器的电路中不可避免存在着噪声扰动和各种时滞.而目前还没有见到关于带混合时滞的随机脉冲系统的无源性研究的相关工作的报道.
忆阻器最终的用途之一是实现人工智能而广泛应用于人类脑神经网络.但目前为止,基于忆阻器的递归神经网络的电路设计与系统建模,以及相关系统的时滞依赖指数无源性和全局指数同步问题都还是公开问题,值得人们进行深入研究.
随着忆阻系统的智能化,人们需要对基于忆阻器的智能系统的协调控制进行研究,建立相应的协议以解决控制系统或其他应用之间存在的通讯网络时滞和信息丢失问题.在实际中,往往会遇到在极短的传输时间需要传输大量数据的问题,怎样减少传感器和控制极点之间的通讯已引起人们极大的兴趣.
基于上述考虑,本文利用Lyapunov稳定性理论、矩阵理论、不等式、模糊化方法等分析工具对忆阻电路系统的建模和控制进行深入系统的研究.研究内容及创新成果包含以下几个方面：
建立了新的基于忆阻器的电路系统,得到了相应的动力学方程,研究了带有不同参数的基于忆阻器的电路系统的同步问题,以及基于忆阻器的不同电路系统的同步问题.
研究了一类基于忆阻器的带混合时滞的随机脉冲分段线性系统的无源性问题.采用一个新的Lyapunov-Krasovskii函数来设计控制器,使得闭环系统是全局无源的.控制器的参数可以通过求解相关的线性矩阵不等式(LMI)获得.所得结果也可应用于一般系统.
讨论了基于忆阻器的递归神经网络的时滞依赖指数无源性问题.在这个过程中,充分考虑了神经元激励函数和时变时滞的信息,与已有相关文献相比,减少了计算量和保守性.同时分析和研究了基于忆阻器的递归神经网络的全局指数同步问题,设计了一种新的基于忆阻器的神经网络,建立了相应的动态方程,并采用并行分布式补偿(PDC)模糊策略来分析此系统,并将所得结论与已有结果进行了比较.
研究了带事件触发控制器的忆阻系统的分布式控制问题,采用一种新的PDC模糊化方法将复杂的忆阻系统线性化为两个子系统,提出了一种事件触发控制策略来更新控制算法从而镇定忆阻系统,并将所得结果扩展到带量化和网络时滞的系统,控制器只在自身触发时更新,这样就减少了通讯量并降低了控制器的更新频率.
这些研究工作深刻揭示了基于忆阻器的电路系统的本质特征.既丰富了忆阻器研究的理论成果,又为基于忆阻器的电路实现与应用技术提供了可靠的依据,具有非常重要的应用价值.
The implementation of memristor provides a novel way to design circuits and achievenew functions. The non-volatile property of memristor provides a good chance to meet thechallenges in front of Neuromorphic Computation. And memristor is a promising solutionfor learning and training of Artificial Neural Networks. Along with the development ofArtificial Neural Networks, the memristor will play a key role in the fuzzy logic, geneticalgorithm and neuro-fuzzy systems. Therefore, modeling and control of memristor-basedcomplex 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 thereconstruction of the data attractors. This is the cause why people plug into the discoveryof chaotic systems. However, as the state-dependence of memristor, there are few works onthe research of synchronization of memristor-based chaotic systems.
Meanwhile, it is necessary to investigate the passive problem for circuit systems toguarantee the inter stability of the whole system. And there exist noise disturbances andvariable time-delays in the memristor-based circuits. Therefore, it is necessary to investigatethe noise disturbances in the process to study the passivity problem of memristor-baseddelayed piecewise linear systems. However, there are no related works on the passivityproblem of stochastic impulsive system with mixed delays.
The terminal implementation of memristor will be in artificial intelligent as ArtificialNeural 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 protocolsto solve the problems of existing delays and data losses in the communication networksbetween the control systems or other applications. Then how to reduce the communicationbetween 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 circuitsystems. The main contents and inventions include:
New memristor-based circuit systems, as well as corresponding dynamical equationsare 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 newLyapunov-Krasovskii functional to make the closed system global passive. The gains of thecontroller can be obtained by the related LMIs. And the obtained results can be extended togeneral systems.
And the delay-dependent exponential passivity problem of memristor-based recurrentneural networks has been discussed with the information of the neural activation functionaand varying-time delays. Compared with existing references, the obtained results reducecomputational burdens and conservativeness. Furthermore, we design a new memristor-based recurrent neural networks, set up correponding dynamical equation, employ PDCfuzzy strategy to study these networks, and investigate the global exponential synchroniza-tion problem of these networks. Furthermore, we compare the obtained results with existingones.
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 intotwo subsystems, then, an event-triggered control strategy is taken to update the controller tostabilize the memristive systems, and the obtained results are extended to the systems withquantization and network induced delays, and the controller is updated only at its own eventtimes, 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 implementationand application of memristor-based circuits.
引文
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