A New Approach to Off-Line Robust Model Predictive Control for Polytopic Uncertain Models

Xianghua Ma,Ning Zhang,Hanqiu Bao

doi:10.3390/designs2030031

Xianghua Ma, Ning Zhang + Show 1 more

Open Access

https://doi.org/10.3390/designs2030031

Copy DOI

Journal: Designs	Publication Date: Aug 20, 2018
Citations: 2	License type: CC BY 4.0

Affiliation: Shanghai Institute of Technology

Abstract

Concerning the robust model predictive control (MPC) for constrained systems with polytopic model characterization, some approaches have already been given in the literature. One famous approach is an off-line MPC, which off-line finds a state-feedback law sequence with corresponding ellipsoidal domains of attraction. Originally, each law in the sequence was calculated by fixing the infinite horizon control moves as a single state feedback law. This paper optimizes the feedback law in the larger ellipsoid, foreseeing that, if it is applied at the current instant, then better feedback laws in the smaller ellipsoids will be applied at the following time. In this way, the new approach achieves a larger domain of attraction and better control performance. A simulation example shows the effectiveness of the new technique.

Highlights

Model predictive control (MPC) has attracted considerable attention, since it is an effective control algorithm to deal with multivariable constrained control problems
We propose a new algorithm with better control performance and larger domains of attraction
We have given a new algorithm for off-line robust MPC

Summary

Introduction

Model predictive control (MPC) has attracted considerable attention, since it is an effective control algorithm to deal with multivariable constrained control problems. Synthesizing robust MPC for constrained uncertain systems has attracted great attention after the nominal MPC. A good technique for robust MPC, requires guaranteed stability, and low computational burden, big (at least desired) domain of attraction, and low performance cost value [9]. The authors in [6] firstly solved a min-max optimization problem in an infinite horizon for systems with polytopic description, by fixing the control moves as a state feedback law that was on-line calculated. The state feedback approach is popular in most of the robust MPC problem, and the full state is assumed to be exactly measured to act as the initial condition for future predictions [10,11,12,13,14]. The symbol * induces e.g., when H and R are symmetric matrices,

Problem Statement

12: Then each time k adopt the following control law

The Improved Off-Line Technique

Example 1

Example 2

Conclusions