The variance and passivity constrained fuzzy control problem for the nonlinear ship steering systems with state multiplicative noises is investigated. The continuous-time Takagi-Sugeno fuzzy model is used to represent the nonlinear ship steering systems with state multiplicative noises. In order to simultaneously achieve variance, passivity, and stability performances, some sufficient conditions are derived based on the Lyapunov theory. Employing the matrix transformation technique, these sufficient conditions can be expressed in terms of linear matrix inequalities. By solving the corresponding linear matrix inequality conditions, a parallel distributed compensation based fuzzy controller can be obtained to guarantee the stability of the closed-loop nonlinear ship steering systems subject to variance and passivity performance constraints. Finally, a numerical simulation example is provided to illustrate the usefulness and applicability of the proposed multiple performance constrained fuzzy control method.

It is known that the vibration impulses occurred from a bearing defect are non-periodic but cyclostationary due to the slippage of rollers. The vibration status is often perceived to be synonymous with quality and thus used for predictive maintenance before breakdown. As a result, the analysis of vibration has been used as a key condition tool for fault detection, diagnosis, and prognosis. Any defect in a bearing causes some vibration that consists of certain frequencies depending on the nature and location of the defect. Although many techniques for time-frequency analysis are reported to measure vibration signals, they were found less efficient in practical applications. For this reason, this article develops an on-line bearing vibration detection and analysis using enhanced fast Fourier transform algorithm. The relation between major vibration frequency and dispersed leakage caused from fast Fourier transform can be induced, and it is then used to establish a mathematical model to find major frequencies of vibration signal. Also, the dispersed energy can be collected to retrieve its original gravitational acceleration. The proposed model is developed using a simple arithmetic operation based on fast Fourier transform so that it is feasible for more efficient calculation in impulse signal analysis. Both measurement calibration and practical results verify that the proposed scheme can achieve accurate, rapid, and reliable outcomes.

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For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

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