A Strategy for the Exact Solution of Multiparametric/Explicit Quadratically Constrained NMPC Problems

Abstract

Multiparametric programming has proven to be an efficient strategy to alleviate the computational burden of solving model predictive control problems online. Recently, it has been shown that through a second-order Taylor approximation to the Basic Sensitivity Theorem, the exact solution of multiparametric/explicit quadratically constrained nonlinear model predictive control problems is enabled. As a result, the state space is nonlinearly partitioned, and the optimal control actions are expressed as nonlinear functions of the states of the system. In this work, an algorithm for the complete exploration of the parameter space and the derivation of the parametric solution of the aforementioned problem is provided. The proposed strategy is utilized to implicitly explore the parameter space by identifying the unique and optimal active sets which describe the parametric solution. The applicability of the presented methodology is demonstrated on a regulation problem of a nonisothermal continuously-stirred tank reactor near an unstable steady-state.