Abstract

Multi-Parametric Programming (mpp) is a widely acknowledged mathematical method for its ability to handle parameter depended optimization problems explicitly. Using this powerful tool, the traditional model predictive control (MPC), which is highly time consuming, can be solved efficiently, so-called explicit MPC (EMPC). Its main advantage is that it obtains the control actions as explicit function of the plant measurements. This allows for the control actions to be obtained on-line via simple function evaluations instead of solving repetitively a computationally demanding on-line optimization. This significant characteristic allows the MPC strategy to be applicable for the fast dynamics, which maybe prohibitive for traditional MPC that relies on optimization methods. This paper aims to study this method from theoretical and practical point of view. The complete unified framework for developing EMPC and its mathematical foundations are studied. Also, in this paper a simple closed form for some matrices well established to achieve low computational complexity in design procedure. Finally the problem of servo system control has been dealt with and thereby the performance and effectiveness of the presented method verified.