Global inverse optimality for a class of recurrent neural networks with multiple proportional delays

This paper formulates two novel theoretical designs of input -to -state stabilizing control for a class of recurrent neural networks with multiple proportional delays. The analysis tool developed in this paper is based on Lyapunov function and inverse optimality method, which does not require solving Hamilton-Jacobi-Bellman equations. Two inverse optimal feedback laws are constructed via the dimensions of state and input, which ensure the input -state stability for the considered system. When the dimensions of state and input are different, we establish a scalar function and give one of the control laws by Sontag's formula. Furthermore, the designs of inverse optimal control reach both global inverse optimality and global asymptotic stability of the system for some meaningful cost functional. Four numerical examples are provided to show the effectiveness of the inverse optimal control.