RBF-ARX model-based robust MPC for nonlinear systems with unknown and bounded disturbance

Abstract

Considering the unknown and bounded disturbance, a RBF-ARX model-based Robust Predictive Control (RBF-ARX-RPC) algorithm for output tracking control without relying on steady state knowledge is proposed for a class of smooth nonlinear systems. From the identified RBF-ARX model, a local linearization state-space model that considers the modeling error and bounded uncertain disturbance is obtained to represent the current behavior of the nonlinear system, and a polytopic uncertain linear parameter varying (LPV) state-space model is built to represent the future system's nonlinear behavior between the output deviation and input increment. Based on the two state-space models, a quasi-min–max robust MPC algorithm is designed for output tracking control of the nonlinear system under the unknown and bounded disturbance, which does not rely on steady state knowledge. Optimization problem of the RBF-ARX-RPC algorithm is finally converted to a convex linear matrix inequalities (LMIs) optimization problem, and the stability is guaranteed by the use of parameter-dependent Lyapunov function and feasibility of the LMIs. The comparative experiments demonstrate the effectiveness of the proposed RBF-ARX-RPC strategy on a continuously stirred tank reactor (CSTR) simulator.