Yuto Asai

We propose new observer-based fuzzy controllers for general Takagi-Sugeno fuzzy system with nonlinear output equations and unmeasurable premise variables. For Takagi-Sugeno fuzzy systems with the unmeasurable premise variables, the separation principle may not hold in general. To overcome this difficulty, we employ the differential mean value theorem and the sector nonlinearity approach to reformulate as an appropriate error system in which the errors between the actual states and its estimates follow. Then, with the state feedback controller and the error system, we have an augmented closed-loop system that can independently and simultaneously analyze the stability of the states and the errors. Since our designed conditions do not require the Lipschitz condition, our approach is more relaxed than the existing approach. Finally, an illustrative example is given to show the effectiveness of the proposed approach.

This paper discusses an observer design and an observer-based controller design for Takagi-Sugeno fuzzy system with unmeasurable premise variables. This case presents a greater challenge compared to fuzzy system with measurable premise variables, as it is difficult to construct a closed-loop system for the state estimation errors. To address this problem, we employ the differential mean value theorem and the sector nonlinearity approach to derive an appropriate new closed-loop system for analyzing the state estimation errors. Moreover, we show that the separation principle holds using the observer obtained above, and an output feedback controller is designed. In this paper, a Lyapunov function incorporating integrals of the membership function is employed to obtain less conservative conditions. The proposed stability conditions are given in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of our approach.

Less conservative and improved stability conditions for Takagi-Sugeno fuzzy systems are newly provided. Extended integral membership function techniques allow us to obtain new stability conditions. Based on such stability conditions, we also provide a state feedback control design for Takagi-Sugeno fuzzy systems. To demonstrate the validity of our given stability conditions, numerical examples are provided. Lastly, we end with concluding remarks.

This paper presents a dynamics-based controller for the longitudinal stabilization of a powered paraglider (PPG). One of the key features of the proposed controller is that it is designed based on the time derivative of the longitudinal dynamics model of the PPG. Since the time derivative of the model contains several nonlinear terms, it is converted into a Takagi-Sugeno fuzzy model. In addition, measurable and unmeasurable variables are clearly distinguished in the proposed approach. Another key feature is that the proposed controller includes only measurable variables. By designing a controller that incorporates all key features, steady flight at a constant altitude is achieved under the effects of updrafts and downdrafts. Furthermore, this controller does not require information on the trimmed input and takes into account the presence of airspeed uncertainty. The effectiveness of the proposed controller is validated through flight simulations using a high-precision PPG simulator.

We discuss an observer design for nonlinear descriptor systems described by Takagi-Sugeno fuzzy descriptor system, which can represent a broader class of systems, including not only differential equations but also algebraic equations, compared to the standard Takagi-Sugeno fuzzy system. The observer design is important to estimate the state of systems because not all states of systems can be measured in many cases. In this paper, we propose a new observer based on a descriptor form and a Lyapunov function candidate structured using integrals of the membership functions to obtain a relaxed observer design condition. Finally, a numerical example is shown to illustrate the comparison of our observer design methods and others based on the conventional Lyapunov functions.