In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local linear input-output relationships. The parallel distributed compensation (PDC) technology and the proportional derivative (PD) feedback scheme are then employed to construct the observer-based fuzzy controller. To solve the problem of unmeasured states, the impulsive phenomenon of singular systems, and the PD scheme’s reasonableness, a novel observer-based fuzzy controller is developed. By using the Lyapunov theory and projection lemma, the stability criteria are built in terms of linear matrix inequalities (LMI). Moreover, the gains of fuzzy controller and fuzzy observer can be calculated synchronously by using convex optimization algorithms. Finally, a biological economic system is provided to verify the effectiveness of the proposed fuzzy control method.

This article addresses the decentralized multi-performance (MP) fuzzy control problem of nonlinear large-scale descriptor (LSD) systems. The considered LSD system contains several subsystems with nonlinear interconnection and external disturbances, and the Takagi–Sugeno fuzzy model (TSFM) is adopted to represent each nonlinear subsystem. Based on the proportional-plus-derivative state feedback (PDSF) scheme, we aim to design a decentralized MP fuzzy controller that guarantees the stabilization, mixed H_∞, and passivity performance control (MHPPC), and the guaranteed cost control (GCC) performance of the closed-loop Takagi–Sugeno LSD (TSLSD) systems. Furthermore, we introduce the Lyapunov stability theory and the free-weighting matrix scheme to analyze the stability of the TSLSD system. The proposed sufficient conditions can be transformed as linear matrix inequality (LMI) forms through Schur’s complement, which can be easily solved with the LMI Toolbox. Finally, to illustrate the proposed approach, two examples and simulation results are presented.

This paper develops a Takagi-Sugeno fuzzy observer gain design algorithm to estimate ship motion based on Automatic Identification System (AIS) data. Nowadays, AIS data is widely applied in the maritime field. To solve the problem of safety, it is necessary to accurately estimate the trajectory of ships. Firstly, a nonlinear ship dynamic system is considered to represent the dynamic behaviors of ships. In the literature, nonlinear observer design methods have been studied to estimate the ship path based on AIS data. However, the nonlinear observer design method is challenging to create directly since some dynamic ship systems are more complex. This paper represents nonlinear ship dynamic systems by the Takagi-Sugeno fuzzy model. Based on the Takagi-Sugeno fuzzy model, a fuzzy observer design method is developed to solve the problem of estimating using AIS data. Moreover, the observer gains of the fuzzy observer can be adjusted systemically by a novel algorithm. Via the proposed algorithm, a more suitable or better observer can be obtained to achieve the objectives of estimation. Corresponding to different AIS data, the better results can also be obtained individually. Finally, the simulation results are presented to show the effectiveness and applicability of the proposed fuzzy observer design method. Some comparisons with the previous nonlinear observer design method are also given in the simulations.

A fuzzy controller design approach is developed in this research for the control problem of a ship’s dynamic path based on automatic identification system (AIS) data. Over the past few decades, the equipment of AISs has been widely applied and mandated on ships. Based on the advantages of AIS data, various valuable applications have been proposed to improve safety problems. However, most of the applications depend on the precise control of the ship’s dynamic behavior. Because of this reason, a fuzzy controller design approach is proposed based on the Takagi–Sugeno fuzzy observer model in this research. Firstly, the ship’s dynamic behavior based on the discrete-time AIS data is estimated and represented by the mathematical model of the fuzzy observer. Based on the fuzzy observer model, a fuzzy controller design approach subject to variance constraint is developed to solve the problem of stochastic disturbance in estimation and control. In accordance with the different application aspects, this approach can not only be applied to improve the estimation performance of the fuzzy observer, but it can also be provided as a controller design scheme for the ship’s dynamic path using AISs data. Finally, simulation results of a group of real AIS data from Kaohsiung Port and the assumed Keelung Port AIS data are applied to verify the effectiveness of the designed fuzzy controller.