An Offline Formulation of MPC for LPV Systems Using Linear Matrix Inequalities

P Bumroongsri

doi:10.1155/2014/786351

Abstract

An offline model predictive control (MPC) algorithm for linear parameter varying (LPV) systems is presented. The main contribution is to develop an offline MPC algorithm for LPV systems that can deal with both time-varying scheduling parameter and persistent disturbance. The norm-bounding technique is used to derive an offline MPC algorithm based on the parameter-dependent state feedback control law and the parameter-dependent Lyapunov functions. The online computational time is reduced by solving offline the linear matrix inequality (LMI) optimization problems to find the sequences of explicit state feedback control laws. At each sampling instant, a parameter-dependent state feedback control law is computed by linear interpolation between the precomputed state feedback control laws. The algorithm is illustrated with two examples. The results show that robust stability can be ensured in the presence of both time-varying scheduling parameter and persistent disturbance.

Highlights

Model predictive control (MPC), known as receding horizon control, is an effective multivariable control algorithm in which a dynamic optimization problem is solved online
The norm-bounding technique is used to derive an offline model predictive control (MPC) algorithm based on the parameterdependent state feedback control law and the parameter-dependent Lyapunov functions
The online computational time is reduced by solving offline the linear matrix inequality (LMI) optimization problems to find the sequences of explicit state feedback control laws

Summary

Introduction

Model predictive control (MPC), known as receding horizon control, is an effective multivariable control algorithm in which a dynamic optimization problem is solved online. It is shown that the proposed MPC algorithm can achieve less conservative results as compared with a robust MPC algorithm derived by using a single Lyapunov function [4] This algorithm includes only time-varying scheduling parameter in the problem formulation so it cannot ensure robust stability in the presence of disturbance. The online computational time is significantly reduced, the disturbance is not taken into account in the offline MPC formulation so robust stability cannot be guaranteed in the presence of disturbance. Unlike Wan and Kothare [22] where only timevarying scheduling parameter is considered in the offline MPC formulation, the main contribution of this paper is to develop an offline MPC algorithm for LPV systems that can deal with both persistent disturbance and time-varying scheduling parameter.

Problem Statement

Offline MPC for LPV Systems with Persistent Disturbances

Examples

Conclusions

Proof of Proposition 3