Multiple Models Approach in Automation: Takagi-Sugeno Fuzzy Systems

Chapter 3

Multiple Model State Estimation

3.1. Introduction

This chapter deals with multiple model state estimation. This involves designing observers, also known as multiple observers, which are constructed by interpolation of local Luenberger observers [LUE 64, ORE 83] through the same activation functions as those used for the multiple model [CHA 02b, MUR 97]. Observer synthesis is an essential topic in automation, as synthesis techniques based on full state feedback require a whole state vector to be available, which is rarely verified in practice. These observers relate to linear or nonlinear models which are subjected to unknown inputs [BOU 00, CHA 08e, DAR 94, GUA 91, KOE 02, KUD 80, SHE 03, VAL 99, XIO 03, YAN 88]. Within the multiple model context, we are going to consider for measurable decision variables, multiple models with uncertainties and also unknown inputs [AKH 03, CHA 09, CHA 10, CHA 12a]. Various techniques are used to perform state estimation.

Some relaxation techniques are used throughout this book, for the synthesis of both observers and controllers.

There is literature on various techniques which can easily be used [GUE 04, LIU 03, TAN 98, TUA 01]. In this book, we have chosen relaxations presented in [LIU 03]. Indeed, a matrix constraint of the form is assured if the following satisfactory matrix conditions are verified:

[3.1]

This matrix constraint is relaxed ...