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.

We propose approaches regarding observer designs for nonlinear systems represented by Takagi-Sugeno fuzzy model in the case that premise variables are unmeasurable. In the framework of Takagi-Sugeno fuzzy system, an observer problem is one of the big challenging tasks because appropriate error closed-loop system is not easily established due to a mismatch problem caused by the unmeasurable premise variables. In the literatures, such a difficulty is limited to the use of a linear output equation. However, in this paper, we show our proposed approach can also handle a nonlinear output equation. Our approach utilizes the differential mean value theorem and this allows to establish a suitable error closed-loop system even with output equations having nonlinearities. The transformed suitable error closed-loop holds convex sum property. Therefore, the stability conditions for the error closed-loop system is obtained in terms of linear matrix inequalities (LMIs) via Lyapunov stability theorem. Finally, a numerical example is provided to show that the main result work properly.

このショートノートでは, 制御行列の不確かさを考慮した高木・菅野ファジィシステムに対するロバストな安定化制御器の設計について議論する. 高木・菅野ファジィシステムは, 幅広い種類のシステムを表現することが可能であり, 非線形システム制御に対して有効である. しかし, システム同定において, 一般的に, 実システムと同一の数式モデルを作成することは不可能である. そのため, 制御器の制御品質を向上させるために, モデリング誤差である不確かさを考慮した高木・菅野ファジィシステムに対する制御器を設計する必要がある. 本研究では, メンバーシップ関数を積分した関数を組み込んだ非二次形式リアプノフ関数を採用し, ロバストな安定化条件を設計する. 最後に, 数値例を用いて本稿で設計した制御器の有効性を検証する.

This paper is concerned with control design methods via a new Lyapunov function for fuzzy descriptor systems. Takagi-Sugeno fuzzy descriptor model, that can represent nonlinear systems, are divided into two families: one with same membership functions in both sides of fuzzy systems and another with different membership functions in right and left side of fuzzy systems. Although many papers propose control designs for the above two systems that are derived from Lyapunov stability theory, they are very conservative because they use a Lyapunov function including a single Lyapunov matrix. In this paper, to design less conservative conditions, we propose new Lyapunov functions with all Lyapunov matrices that are multiple. Finally, numerical examples are given to show the effectiveness of our methods.

This paper is on the issues of designing fuzzy controllers for Takagi-Sugeno fuzzy systems. Many works on the stability and stabilization problems on Takagi-Sugeno fuzzy systems have been done. In the literature, stabilization conditions for Takagi-Sugeno fuzzy system have been improved and their feasibility range has been extended. However, there remains room for reducing the conservativeness for such stabilization conditions. In this paper, we propose a new fuzzy controller design via higher order derivatives of a Lyapunov function with an integral of the membership functions, which drastically reduces the existing conservative stabilization conditions. Finally, a comparison with previous studies is presented to demonstrate the effectiveness of our proposed control method.

このショートノートでは, 高木・菅野ファジィシステムの 𝐻∞ 制御とコスト保証制御を掛け合わせた新しい制御設計を提案する. 𝐻∞ 制御は, システムに入る外乱を抑制し, コスト保証制御は制御器の制御性能を向上させる. 高木・菅野ファジィシステムの制御設計については, これまでに多くの論文で議論されているが, この混合問題はまだ考慮されていない. このショートノートでは, 制御性能を向上させることができるコスト保証制御に関わる評価関数の上限を下げるアルゴリズムを提案する. 本制御器は, 𝐻∞ 制御とともに, 制御性能だけでなく外乱の抑制にも配慮した制御設計手法を採用している. 最後に, 数値例を用いて提案された設計手法の有効性を示す.

This paper proposes a new control design method via two techniques to decrease the conservativeness in control design conditions for Takagi-Sugeno fuzzy systems that can represent a wide class of nonlinear systems. The first technique we employ is to use higher order derivatives of Lyapunov function that is shown to reduce the conservativeness in the literature. The second one is a switching approach that takes advantages of a property of the membership function. In this paper, we provide control design methods and their less conservative conditions based on the above-mentioned techniques. The proposed control design conditions are independent of the membership function and are written in a linear matrix inequality form. Finally, Numerical examples illustrate the effectiveness of the proposed control methods by comparing with the existing methods.

We provide a less conservative approach for the stability analysis of Takagi–Sugeno fuzzy systems via multiple Lyapunov function with an integral of the membership function. In many papers, fuzzy Lyapunov function and the stability of fuzzy systems have been discussed. Since they assumed the upper/lower bounds of the derivative of the membership function derived from fuzzy Lyapunov function, they basically give local stability conditions. In this paper, we employ a Lyapunov function constructed with an integral of the membership function, from which less conservative stability conditions have been obtained in the literature. Furthermore, by combining linear fractional transformation (LFT) method and S-procedure method, we obtain a global asymptotic stability condition of fuzzy systems. Finally, an example is shown to confirm the advantage of the proposed method.