Matrix polynomial

Physics

Polynomial matrix

Sylvester matrix

Mathematics

Economic growth

Gene

Sylvester equation

Recurrent neural network

Mathematical analysis

Artificial intelligence

Eigenvalues and eigenvectors

Economics

Control (management)

Chemistry

Convergence (economics)

Computer science

Quantum mechanics

Differential equation

Applied mathematics

Control theory (sociology)

Artificial neural network

Biochemistry

Robustness (evolution)

Polynomial

Algebraic number

IEEE Transactions on Cybernetics

Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.

A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation