Enlarging the Domain of Attraction of Predictive Control for Constrained Affine Nonlinear Systems

A new method for enlarging the domain of attraction of dual-mode nonlinear model predictive control (NMPC) is developed for a constrained affine nonlinear system by adopting the extended terminal constraint set and its admissible set. First, an optimization method for calculating a maximal control invariant set with respect to a feedback linearizing control law and a polytope linear difference inclusion (PLDI)for an affine nonlinear system is presented. Accordingly, a switching control strategy of the control invariant set is designed to extend the terminal constraint set. Second, interval arithmetic is introduced to compute the N step admissible sets of the extended terminal constraint set off-line, and then the resulting dual-mode controller with a one-step predictive horizon can guarantee the stability and enlargement of the domain of attraction of predictive control by considering this sequence as an attraction domain of initial states in the optimization problem. Finally, the method is tested in a typical nonlinear process control system - a continuously stirring tank reactor (CSTR)； the results show the feasibility of the proposed method.