Explicit solutions for nonlinear model predictive control: A linear mapping approach

A methodology for the construction of an explicit nonlinear control law approximating nonlinear constrained finite-time optimal control (CFTOC) is presented. This is achieved by means of a modelling technique that permits the use of an approximate mapping of a general nonlinear system. A set of piecewise affine (PWA) systems is created such that the information of the nonlinear structure of the original system is maintained. The key advantages of this methodology are two-fold: Firstly, having an explicit solution of the CFTOC problem permits the direct implementation of traditionally computational-wise too complex optimal control techniques for real-time applications. Secondly, taking advantage of MPC´s systematic fashion to perform nonlinear control synthesis eases the design of an optimal control law. The proposed theory is illustrated by simulation on the Duffing oscillator.