A Summary of Dynamic Output Feedback Robust MPC for Linear Polytopic Uncertainty Model with Bounded Disturbance

Baocang Ding,Jianchen Hu,Xiaoming Tang

doi:10.1155/2020/3830724

Abstract

This paper is the summary and enhancement of the previous studies on dynamic output feedback robust model predictive control (MPC) for the linear parameter varying model (described in a polytope) with additive bounded disturbance. When the state is measurable and there is no bounded disturbance, the robust MPC has been developed with several paradigms and seems becoming mature. For the output feedback case for the LPV model with bounded disturbance, we have published a series of works. Anyway, it lacks a unification of these publications. This paper summarizes the existing results and exposes the ideas in a unified framework. Indeed there is a long way to go for the output feedback case for the LPV model with bounded disturbance. This paper can pave the way for further research on output feedback MPC.

Highlights

It is widely recognized that linear parameter varying (LPV) model, whose system matrices lie in the polytope, is a good tool for representing the nonlinearity and uncertainty. e well-known Takagi–Sugeno (T-S) model, often when the stability is considered, can be considered as the LPV model. erefore, it is not surprising that there are a lot of research works on the LPV model-based and T-S modelbased controls
We rearrange the results of output feedback model predictive control (MPC) for the LPV model during these years, compromising the above demerits in the existing works
We found that with only 2 controller parameters 􏼈Lc, Fx􏼉, for (1), it is more difficult to find the feasible solution to the optimization problem of output feedback MPC

Summary

Introduction

It is widely recognized that linear parameter varying (LPV) model, whose system matrices lie in the polytope, is a good tool for representing the nonlinearity and uncertainty. e well-known Takagi–Sugeno (T-S) model (see, e.g., [1, 2]), often when the stability is considered, can be considered as the LPV model. erefore, it is not surprising that there are a lot of research works on the LPV model-based and T-S modelbased controls. E additive bound disturbance, with its real-time value arbitrarily changing, without useful statistics, is another widely accepted uncertainty description. Is paper considers the above LPV model (including T-S model) with additive bound disturbance. We have published several works on output feedback MPC, there lacks a unified and updated framework. We rearrange the results of output feedback MPC for the LPV model during these years, compromising the above demerits in the existing works. We think that this is useful for future research; it is a guideline, and a summary for readers. (ix) ★: this symbol induces a symmetric structure in any square matrix (x) ∗: a value with superscript ∗ means that it is the solution of the optimization problem

Dynamic Output Feedback Robust MPC Problem

General Optimization Problem

Solutions to Output Feedback MPC

Conclusion