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

Abstract

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.