Sylvester equation

Matrix polynomial

Gene

Physics

Polynomial matrix

Mathematical analysis

Recurrent neural network

Artificial intelligence

Eigenvalues and eigenvectors

Economics

Chemistry

Sylvester matrix

Control (management)

Convergence (economics)

Applied mathematics

Mathematics

Computer science

Control theory (sociology)

Economic growth

Artificial neural network

Biochemistry

Quantum mechanics

Robustness (evolution)

Differential equation

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