A finite-time recurrent neural network for solving online time-varying Sylvester matrix equation based on a new evolution formula. (English) Zbl 1380.34047
Summary: Sylvester equation is widely used to study the stability of a nonlinear system in the control field. In this paper, a finite-time Zhang neural network (FTZNN) is proposed and applied to online solution of time-varying Sylvester equation. Differing from the conventional accelerating method, the design of the proposed FTZNN model is based on a new evolution formula, which is presented and studied to accelerate the convergence speed of a recurrent neural network. Compared with the original Zhang neural network (ZNN) for time-varying Sylvester equation, the FTZNN model can converge to the theoretical time-varying solution within finite time, instead of converging exponentially with time. Besides, we can obtain the upper bound of the finite convergence time for the FTZNN model in theory. Simulation results show that the proposed FTZNN model achieves the better performance as compared with the original ZNN model for solving online time-varying Sylvester equation.
MSC:
| 34B45 | Boundary value problems on graphs and networks for ordinary differential equations |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
Keywords:
Zhang neural network; time-varying Sylvester equation; finite-time convergence; evolution formula; upper boundReferences:
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