Control Design for Fuzzy Systems Based on Relaxed Nonquadratic Stability and H∞ Performance Conditions

Dept. of Autom., Hangzhou Dianzi Univ., Zhejiang
IEEE Transactions on Fuzzy Systems (Impact Factor: 8.75). 04/2007; 15(2):188-199. DOI: 10.1109/TFUZZ.2006.879996
Source: IEEE Xplore


In this paper, new approaches to Hinfin controller design for a class of discrete-time nonlinear fuzzy systems are proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, two relaxed conditions of nonquadratic stability with H infin norm bound are presented for this class of systems. The two relaxed conditions are shown to be useful in designing fuzzy control systems. By introducing some additional instrumental matrix variables, the two relaxed conditions are used to develop Hinfin controllers. In the control design, the first relaxed condition has fewer inequality constraints, but only admits a common additional matrix variable while the second one can admit multiple additional matrix variables. Finally, two examples are given to demonstrate the applicability of the proposed approach

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    • "The most popular type of fuzzy controller is the state-feedback fuzzy controller (referred to as fuzzy controller hereafter), which is employed to close the feedback loop for the control process. Other fuzzy controllers, such as the adaptive fuzzy controller [7]–[18], decentralized fuzzy controller [19], fuzzy sliding-mode controller [20]–[27], fuzzy controller with fault-tolerant design [28], fuzzy controller for time-delay systems [29], H ∞ fuzzy controller [30], [31], output-feedback fuzzy controller [32], switching fuzzy controller [33]–[39], sampled-data fuzzy controller [40]–[45], and 2-D fuzzy controller [46], can also be found in the literature. "
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    ABSTRACT: This paper investigates the stability of a polynomial-fuzzy-model-based (PFMB) control system formed by a nonlinear plant represented by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. Three cases of polynomial fuzzy controllers are proposed for the control process with the consideration of a matched/mismatched number of rules and/or premise membership functions, which demonstrate different levels of controller complexity, design flexibility, and stability analysis results. A general polynomial Lyapunov function candidate is proposed to investigate the system stability. Unlike the published work, there is no constraint on the polynomial Lyapunov function candidate, which is independent of the form of the polynomial fuzzy model. Thus, it can be applied to a wider class of PFMB control systems and potentially produces more relaxed stability analysis results. Two-step stability conditions in terms of sum-of-squares (SOS) are obtained to numerically find a feasible solution. To facilitate the stability analysis and relax the stability analysis result, the boundary information of membership functions is taken into account in the stability analysis and incorporated into the SOS-based stability conditions. Simulation examples are given to illustrate the effectiveness of the proposed approach.
    IEEE Transactions on Fuzzy Systems 06/2015; 23(3):511-524. DOI:10.1109/TFUZZ.2014.2315674 · 8.75 Impact Factor
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    • "Takagi-Sugeno(T-S) model fuzzy systems have been extensively studied in the past decades since T-S fuzzy models can be used to effectively represent a large class of nonlinear systems. Many controller design problems for T-S model fuzzy systems have been considered in the literature [16]– [19]. The most frequently used control design method is the so-called parallel distribution compensation (PDC), by which the controller shares the same fuzzy premise variables and membership functions with the T-S fuzzy plant. "
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    ABSTRACT: This paper considers the H∞ control problem for discrete-time Takagi-Sugeno (T-S) model fuzzy systems with event-triggered output feedback. The measurement output is transmitted to a fuzzy controller when the output error exceeds a pre-given threshold. The parallel distribution compensation (PDC) can not be used for controller design since the controller may not receive enough information about premise variables of the plant due to the event-triggered transmission scheme. A fuzzy dynamical output feedback controller is proposed to regularly generate the control input, which makes the controlled system stable with a certain H∞ disturbance attenuation level. A numerical example is given to show the effectiveness of the proposed approach.
    Industrial Electronics Society, IECON 2013 - 39th Annual Conference of the IEEE; 01/2013
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    • "However, a more relaxed stability approach that is developed for T–S fuzzy systems can be used to this end (see, for instance, [1]–[3], [7], [9], [13]–[17], [20], [25]–[27], [30], [31], [34], [35], and [37]–[42]). Then, the following controller can be readily obtained [6], [23] "
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    ABSTRACT: The exact output regulation for Takagi–Sugeno (T–S) fuzzy models depends on two conditions: 1) The local steady-state zero-error manifolds have to be the same for every local subsystem, and 2) the local input matrices have to be the same for every local subsystem included in the T–S fuzzy model. These conditions are difficult to satisfy in general. In this paper, those conditions are relaxed by solving the fuzzy regulation problem directly on the overall T–S fuzzy model, instead of constructing the fuzzy regulator on the basis of linear local controllers. By considering the fuzzy model as a special class of linear time-varying systems, existence conditions are rigorously derived. These new conditions, which can be solved by means of any mathematical software, depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and/or the exosystem. Two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach.
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