Model Predictive Control of Linear Systems over Networks with State and Input Quantizations

Xiao-Ming Tang,Hong-Chun Qu,Hao-Fei Xie,Ping Wang

doi:10.1155/2013/492804

Abstract

Although there have been a lot of works about the synthesis and analysis of networked control systems (NCSs) with data quantization, most of the results are developed for the case of considering the quantizer only existing in one of the transmission links (either from the sensor to the controller link or from the controller to the actuator link). This paper investigates the synthesis approaches of model predictive control (MPC) for NCS subject to data quantizations in both links. Firstly, a novel model to describe the state and input quantizations of the NCS is addressed by extending the sector bound approach. Further, from the new model, two synthesis approaches of MPC are developed: one parameterizes the infinite horizon control moves into a single state feedback law and the other into a free control move followed by the single state feedback law. Finally, the stability results that explicitly consider the satisfaction of input and state constraints are presented. A numerical example is given to illustrate the effectiveness of the proposed MPC.

Highlights

Model predictive control (MPC) commonly refers to a class of computer control algorithms that use an explicit process model to forecast the future response of a plant [1]
In recent decades, it has a great improvement in theoretical research; various methodologies have been addressed and developed, such as dynamic matrix control (DMC), generalized predictive control (GPC), and robust MPC
From the 1990s, the main stream of the theoretical research about MPC has been turned to the synthesis approach, which means that the MPC controller is synthesized so that the closed-loop system is stable whenever the optimization problem is feasible

Summary

Introduction

Model predictive control (MPC) commonly refers to a class of computer control algorithms that use an explicit process model to forecast the future response of a plant [1]. The on-line computational burden can be significantly reduced Another procedure of synthesis approach of MPC is to add free control moves before the linear state feedback law, instead of a single state feedback. Reference [14] generalizes the results of [13] to the multi-input-multi-output (MIMO) systems and the output feedback control and converts the quantized quadratic stabilization problem into the robust control problem by using the sector bound method. Based on the results in [14], a robust MPC strategy is proposed to deal with the stabilization of NCS with quantized control input in [16] and a simple dynamic scaling method for a logarithmic quantizer based output feedback controller is given in [17]. The superscript T denotes the transpose for vectors or matrices. x(k + i | k) is the value of vector x at a future time k + i predicted at time k

System Description

Stabilization Using Networked MPC

Numerical Example

Findings

Conclusions