Stability and Performance Analysis of Polynomial Fuzzy-Model-Based Control Systems and Interval Type-2 Fuzzy Logic Systems

Student thesis: Doctoral ThesisDoctor of Philosophy


The main research objective in this thesis is to investigate the stability and performance of the interval type-2 (IT2) polynomial-fuzzy-model-based (PFMB) control system. PFMB control scheme has been developed recently around 2009 and demonstrates more potential than the traditional Takagi-Sugeno fuzzy-model-based (T-S FMB) control approach to represent the nonlinearities in the plant. Meanwhile, the IT2 fuzzy logic has also been proposed to incorporate uncertainties of the nonlinear systems into the membership functions directly. Through the IT2 PFMB control design approach, both the nonlinearity and the uncertainty in the system can be handled well. The control performance and the relaxation of stability conditions of IT2 PFMB control systems are studied and investigated in the thesis. The main contribution of the thesis is summarized in three tasks and presented as following:

In the first task in Chapter 3, the stability conditions of the PFMB systems equipped with mismatched IT2 membership functions are investigated. Unlike the membership-function-independent (MFI) methods, the information and properties of IT2 membership functions are considered in the stability analysis and contained in the stability conditions in terms of sum-of-squares (SOS) based on the Lyapunov stability theory. Three methods, demonstrating their own merits, are proposed to conduct the stability analysis for the IT2 PFMB control systems and all of the methods can achieve feasible control results. All the three approaches are well explained, which offers the reader systematic ways to include the information of the membership functions into the analysis. In addition, all the approaches are compared and the pros and cons are presented to help the reader choose the most appropriate approach in the applications.

In the second task presented in Chapter 4, the membership-functions-dependent (MFD) methods have been proceeded to the tracking control problems and the output feedback tracking issues of IT2 PFMB fuzzy control systems are investigated. The output-feedback IT2 polynomial fuzzy controller connected with the nonlinear plant in a closed loop drives the system states of the nonlinear plant to track those of the stable reference model. The system stability is investigated based on the Lyapunov stability theory under the SOS-based analysis approach and the SOSbased stability conditions are derived subject to a prescribed H1 performance. Like in the first work, the information of membership functions is also included in the analysis to facilitate the analysis and help improve the tracking performance in terms of H1 performance.

Considering the implementation of the mentioned control schemes on digital computers, the sampled-data control systems are investigated as the last work in the thesis, which is presented in Chapter 5. In this task, the IT2 PFMB tracking control system is extended to the sampled-data based one. Through using the sampled output of both the control system and the reference system, an IT2 polynomial sampled-data based output feedback fuzzy controller can be designed to ful ll the tracking control task, the stability conditions can be obtained in terms of SOS and the tracking error is attenuated by the H1 performance index. As did in the previous two works, the information of the IT2 membership functions is used to relax the stability conditions and improve the tracking performance.

The approaches proposed in the thesis to relax the stability conditions as well as to improve the tracking performance of the IT2 PFMB control systems are proved through the Lyapunov based stability theory. Meanwhile, simulation examples are provided to demonstrate and verify the theoretical analysis.
Date of Award2018
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorHongbin Liu (Supervisor) & Hak-Keung Lam (Supervisor)

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