Explicit nonlinear predictive control for a magnetic levitation system

The paper presents a methodology for the construction of an explicit nonlinear control law via approximation of the nonlinear constrained finite‐time optimal control (CFTOC). This is achieved through an approximate mapping of a general nonlinear system in a set of linear piecewise affine (PWA) systems. The key advantages of this methodology are two‐fold. First, the construction of an analytic solution of the CFTOC problem leads to an efficient explicit implementation. Second, by taking advantage of model predictive control's systematic fashion to handle constraints, an improved performance can be obtained for the closed‐loop system. The proposed theory is applied in real‐time for a system with fast dynamics: a magnetic levitation benchmark.