Neural-model based robust H∞ controllers for discrete-time nonlinear systems: an BMI approach

In this paper, a neural-model based robust H_∞ control design for a discrete-time nonlinear system is addressed. The design approach is to approximate the nonlinear system with a neural network with biases of which the activation functions satisfy the sector conditions. A novel neural network model named as standard neural network model (SNNM) with uncertainty is advanced for describing this class of approximating neural networks with biases. And a state-feedback control law is designed for the SNNM with real parametric uncertainty, such that L₂ gain of the closed-loop system is minimal. The approach is based on the robust L₂ gain (i.e. robust H_∞, performance) analysis of the Lure system using the common Lyapunov approach. The control design equations are shown to be a set of bilinear matrix inequalities (BMIs) which can be solved by an improved iterative algorithm. Finally, a detailed design procedure of the control law for the nonlinear system is provided.