Recurrent Neural Networks were invented a long time ago, and dozens of different architectures have been published. In this paper we generalize recurrent architectures to a state space model, and we also generalize th...Recurrent Neural Networks were invented a long time ago, and dozens of different architectures have been published. In this paper we generalize recurrent architectures to a state space model, and we also generalize the numbers the network can process to the complex domain. We show how to train the recurrent network in the complex valued case, and we present the theorems and procedures to make the training stable. We also show that the complex valued recurrent neural network is a generalization of the real valued counterpart and that it has specific advantages over the latter. We conclude the paper with a discussion of possible applications and scenarios for using these networks.展开更多
In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition,...In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
In this paper, an adaptive neuro-control structure for complex dynamic system is proposed. A recurrent Neural Network is trained-off-line to learn the inverse dynamics of the system from the observation of the input-o...In this paper, an adaptive neuro-control structure for complex dynamic system is proposed. A recurrent Neural Network is trained-off-line to learn the inverse dynamics of the system from the observation of the input-output data. The direct adaptive approach is performed after the training process is achieved. A lyapunov-Base training algorithm is proposed and used to adjust on-line the network weights so that the neural model output follows the desired one. The simulation results obtained verify the effectiveness of the proposed control method.展开更多
文摘Recurrent Neural Networks were invented a long time ago, and dozens of different architectures have been published. In this paper we generalize recurrent architectures to a state space model, and we also generalize the numbers the network can process to the complex domain. We show how to train the recurrent network in the complex valued case, and we present the theorems and procedures to make the training stable. We also show that the complex valued recurrent neural network is a generalization of the real valued counterpart and that it has specific advantages over the latter. We conclude the paper with a discussion of possible applications and scenarios for using these networks.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61374094 and 61503338)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.
文摘In this paper, an adaptive neuro-control structure for complex dynamic system is proposed. A recurrent Neural Network is trained-off-line to learn the inverse dynamics of the system from the observation of the input-output data. The direct adaptive approach is performed after the training process is achieved. A lyapunov-Base training algorithm is proposed and used to adjust on-line the network weights so that the neural model output follows the desired one. The simulation results obtained verify the effectiveness of the proposed control method.
