dc.description.abstract | Observer and controller design for nonlinear systems is categorized as a great challenge for researchers. In general, because a nonlinear system may have a complex form, observer and controller design may be difficult. Therefore, transforming the nonlinear system into other models is always necessary. In this study, the nonlinear system is transformed into four models which are the discrete time uncertain T-S fuzzy model, uncertain polynomial model, uncertain polynomial T-S fuzzy model and continuous time T-S fuzzy system with the disturbance, then the observer and controller are synthesized for these system models instead of the original nonlinear systems. Particularly, in this dissertation, the observer is synthesized for the discrete time uncertain T-S fuzzy systems, uncertain polynomial T-S fuzzy system; and the observer-based controller is designed for the continuous T-S fuzzy systems with disturbances and the uncertain polynomial systems. It is noted that with the existing of the uncertainties and disturbances, synthesizing the observer and controller for the nonlinear systems becomes much more difficult. Because the uncertainties/disturbances always make the estimation errors and the states be unable to converge zero asymptotically.
In this dissertation, the contributions are presented in four main chapters. In Chapter 3, a new methodology based on the unknown input method is proposed for synthesizing the observer to estimate the un-measurable state variables of the discrete time uncertain T-S fuzzy system. This new approach allows us not only eliminate the effects of uncertainties but also make the estimated states approach to real states asymptotically without knowing the upper bounds of the uncertainties. Moreover, both premise variables are dependent and independent on the unmeasured state variables are investigated for the discrete time uncertain T-S fuzzy system. Additionally, the non-common quadratic Lyapunov function is employed to make the conditions for the observer design be more relaxed. In Chapter 4, a new approach to design the observer for uncertain polynomial T-S fuzzy system is proposed. The upper bounds of the uncertainties are not given in advance. A novel polynomial observer form is proposed to estimate the un-measurable states and eliminate completely the influences of the uncertainties without designing a controller and knowing the upper bounds of the uncertainties. Moreover, with the aids of the non-common Lyapunov function and SOS technique, the sufficient conditions for observer synthesis are derived.
Furthermore, new methodology to synthesize the observer-based controller for the uncertain polynomial system is established in Chapter 5. The uncertain polynomial system is transformed into the polynomial system with the disturbance then the observer-based controller is designed for this system. The novel control process based on the unknown input method is proposed to estimate states and stabilize the system in which the upper bounds of uncertainties and all/some states are unknown. Besides, a new framework of the observer is synthesized to estimate the un-measurable states and the disturbances simultaneously. In Chapter 6, the observer-based controller is synthesized to the continuous T-S fuzzy system with the presence of the disturbance. The class of the disturbance is significantly enlarged because it does not need to satisfy the strict constraints such as bounded, finite derivative is equal to zero or generated from the exogenous model. A new form of the state and disturbance observer is proposed to estimate the unmeasurable states and disturbance simultaneously. The controller incorporating with the state and disturbance observer is designed to counteract to the impacts of the disturbance and stabilize the system.
In conclusion, this dissertation proposed several methods to synthesize observer and controller for the uncertain nonlinear system. On the basis of Lyapuov theory, the conditions of design observer and controller are derived in term of LMIs (Linear Matrix Inequalities) and SOS (Sum of Squares) which can be solved by LMIs tool and SOS tools in Matlab. Finally, several examples are shown to illustrate the effectiveness and advantages of the proposed methods. | en_US |