A recurrent neural network (RNN) can generate a sequence of patterns as the temporal evolution of the output vector. This paper focuses on a continuous-time RNN model with a piecewise-linear activation function that h...
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A recurrent neural network (RNN) can generate a sequence of patterns as the temporal evolution of the output vector. This paper focuses on a continuous-time RNN model with a piecewise-linear activation function that has neither external inputs nor hidden neurons, and studies the problem of finding the parameters of the model so that it generates a given sequence of bipolar vectors. First, a sufficient condition for the model to generate the desired sequence is derived, which is expressed as a system of linear inequalities in the parameters. Next, three approaches to finding solutions of the system of linear inequalities are proposed: One is formulated as a convex quadratic programming problem and others are linear programming problems. Then, two types of sequences of bipolar vectors that can be generated by the model are presented. Finally, the case where the model generates a periodic sequence of bipolar vectors is considered, and a sufficient condition for the trajectory of the state vector to converge to a limit cycle is provided.(c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).
The article introduces a new technique for process modeling. On the basis of the fact that once nonlinear problem is modeled by piecewise-linear model, it can be solved by many efficient techniques, the result of intr...
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ISBN:
(纸本)9781479930098
The article introduces a new technique for process modeling. On the basis of the fact that once nonlinear problem is modeled by piecewise-linear model, it can be solved by many efficient techniques, the result of introduced technique provides a set of linear equations. Each of these equations is valid in some region of state space and together, they approximate whole nonlinear process.
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