Robust H∞ control for uncertain delayed nonlinear systems based on standard neural network models

A neural-network-based robust output feedback H∞ control design is suggested for control of a class of nonlinear systems both with time delays and with uncertainties. In this paper, a full-order dynamic output feedback controller is designed for the delayed uncertain nonlinear system approximated by the neural network (e.g. multilayer perceptron, recurrent neural network, etc.), of which the activation functions satisfy the sector conditions. The closed-loop neural control system is transformed into a novel neural network model both with uncertainties and with time delays termed standard neural network model (SNNM). Based on the optimal robust H∞ performance analysis of the SNNM, the parameters of output feedback controllers can be obtained by solving some linear matrix inequalities (LMIs). The optimal H∞ controller ensures the robust global asymptotic stability of the closed-loop system and eliminates the effect of approximation errors, parametric uncertainties, and external disturbances. Finally, a simple example is presented to illustrate the effectiveness and the applicability of the proposed design approach.