Toshiaki Seo

The University of Electro-Communications, Tokyo, Tokyo-to, Japan

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Publications (3)3.01 Total impact

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    ABSTRACT: This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.
    IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics: a publication of the IEEE Systems, Man, and Cybernetics Society 04/2012; 42(5):1330-42. · 3.01 Impact Factor
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    ABSTRACT: This paper presents a sum of squares (SOS, for brevity) based observer design for a more general class of polynomial fuzzy systems with the polynomial matrices A<sub>i</sub>(x(t)) and B<sub>i</sub>(x(t)) that are permitted to be dependent of the states x(t). First, we briefly summarize previous works on SOS-based observer designs for two limited classes of polynomial fuzzy systems. To overcome the difficulty of the fact that does not realize the so-called separation principle design for the more general class, this paper provides a practical design procedure of a polynomial fuzzy controller and a polynomial fuzzy observer without lack of guaranteeing the stability of the overall control system in addition to converging state estimation error (via the observer) to zero. The design approach discussed in this paper is more general than the existing LMI approaches (to T-S fuzzy controller and observer designs) and also than the previous SOS-based observer designs. To illustrate the validity of the design approach, a design example is provided. The example shows the utility of our SOS approach to the polynomial fuzzy observer-based control for the more general class of polynomial fuzzy systems.
    American Control Conference (ACC), 2011; 08/2011
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    ABSTRACT: This paper presents a polynomial fuzzy observer design for a wider class of polynomial fuzzy systems via a sum of squares (SOS, for brevity) approach. The proposed SOS-based framework provides a number of innovations and improvements over the existing LMI-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results for a class of polynomial fuzzy systems that is more general representation of the well-known T-S fuzzy system. Next, we propose a polynomial fuzzy observer to estimate states in a wider class of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions is that they realize the so-called separation principle, that is, that a polynomial fuzzy controller and observer for this class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state estimation error (via the observer) to zero. The design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recent developed SOSTOOLS and a semidefinite program (SDP) solver, respectively. To illustrate the validity and applicability of the proposed approach, a design example is provided. The example demonstrates advantages of the SOS-based approach for the existing LMI approaches to T-S fuzzy observer designs.
    FUZZ-IEEE 2011, IEEE International Conference on Fuzzy Systems, Taipei, Taiwan, 27-30 June, 2011, Proceedings; 01/2011