A New Optimal Control Formulation to Ensure the Stability of NMPC Systems

Abstract

Nonlinear model predictive control (NMPC) has been considered as a promising control algorithm, since a rigorous model can be explicitly employed and state variable restrictions ensured by formulating inequality constraints. However, due to the nonlinear problem formulation, it is difficult to analyze the stability properties of NMPC systems. In this study we propose a new formulation of the optimal control problem to ensure the stability of NMPC systems. Auxiliary state variables and linear state equations will be introduced and their eigenvalues optimized in the dynamic optimization framework. System state variables will be constrained by these auxiliary variables so that they will conform to the stability properties of the auxiliary variables. Features of this stabilization approach are analyzed. Results of case studies indicate satisfactory effectiveness of the proposed NMPC.