Nonlinear system modeling and robust predictive control based on RBF-ARX model

An integrated modeling and robust model predictive control (MPC) approach is proposed for a class of nonlinear systems with unknown steady state. First, the nonlinear system is identified off-line by RBF-ARX model possessing linear ARX model structure and state-dependent Gaussian RBF neural network type coefficients. On the basis of the RBF-ARX model, a combination of a local linearization model and a polytopic uncertain linear parameter-varying (LPV) model are built to approximate the present and the future system's nonlinear behavior, respectively. Subsequently, based on the approximate models, a min–max robust MPC algorithm with input constraint is designed for the output-tracking control of the nonlinear system with unknown steady state. The closed-loop stability of the MPC strategy is guaranteed by the use of parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). Simulation study to a NOx decomposition process illustrates the effectiveness of the modeling and robust MPC approaches proposed in this paper.