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A new type of activation function, named Li activation function, is used in gradient-based neural network (GNN) to solve Lyapunov matrix equation. With this activation function, theoretical analysis shows that GNN can converge in finite time, while it can converge only in infinite time with two conventional activation functions — linear and power-sigmoid. Computer simulation results confirm that GNN with Li activation function can not only globally converge to the solution of the Lyapunov matrix equation but also converge in finite time. GNN with the conventional two activation functions are also simulated as a contrast.

Gradient-based Neural Network for Online Solution of Lyapunov Matrix Equation with Li Activation Function