Maximal Overlapped-rules Group Research Articles

Fuzzy Emergency Model and Robust Emergency Strategy of Supply Chain System under Random Supply Disruptions

For random distributors under supply disruptions caused by emergency incidents, a fuzzy emergency model and a robust emergency strategy of the supply chain system are studied. First, for a kind of supply chain system composed of a strategic manufacturer, a backup manufacturer, and multiple distributors, the basic emergency models, including the inventory models and a total cost model, are constructed under random supply disruptions. Then, based on the Takagi‐Sugeno fuzzy system, the basic emergency models of the supply chain system are converted into a discrete switching model, which can realize soft switching among the basic emergency models. Furthermore, according to the different inventory levels, the strategic manufacturer’s production strategies and the distributors’ ordering strategies are designed to reduce the inventory costs of the node enterprises in supply chain system. Second, by defining a discrete piecewise Lyapunov function in each maximal overlapped‐rules group, a new fuzzy robust emergency strategy for the supply chain system is proposed through the principle of parallel distributed compensation. This emergency strategy can not only restore the impaired supply chain to the normal operation state but also keep the total cost of the supply chain at a low level and guarantee the robust stability of the emergency supply chain system. Finally, the simulation results illustrate the effectiveness of the proposed fuzzy robust emergency strategy of the supply chain system.

Fuzzy Control Model and Simulation for Nonlinear Supply Chain System with Lead Times

A new fuzzy robust control strategy for the nonlinear supply chain system in the presence of lead times is proposed. Based on Takagi-Sugeno fuzzy control system, the fuzzy control model of the nonlinear supply chain system with lead times is constructed. Additionally, we design a fuzzy robust H∞ control strategy taking the definition of maximal overlapped-rules group into consideration to restrain the impacts such as those caused by lead times, switching actions among submodels, and customers’ stochastic demands. This control strategy can not only guarantee that the nonlinear supply chain system is robustly asymptotically stable but also realize soft switching among subsystems of the nonlinear supply chain to make the less fluctuation of the system variables by introducing the membership function of fuzzy system. The comparisons between the proposed fuzzy robust H∞ control strategy and the robust H∞ control strategy are finally illustrated through numerical simulations on a two-stage nonlinear supply chain with lead times.

Stability and stabilization of discrete T-S fuzzy time-delay system based on maximal overlapped-rules group

The problems of stability and stabilization for the discrete Takagi-Sugeno (T S) fuzzy time-delay system are investigated. By constructing a discrete piecewise Lyapunov-Krasovskii function (PLKF) in each maximal overlapped-rules group (MORG), a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved. Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme, and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed. The above two sufficient conditions only require finding common matrices in each MORG. Compared with the common Lyapunov-Krasovskii function (CLKF) approach and the fuzzy Lyapunov-Krasovskii function (FLKF) approach, these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved. Finally, simulation examples show that the proposed PLKF approach is effective.

Robust Stabilization for Discrete Uncertain Takagi–Sugeno Fuzzy Systems Based on a Piecewise Lyapunov Function

This article investigates the robust H∞ fuzzy output-feedback control problem for a discrete Takagi–Sugeno (T–S) fuzzy system with uncertainties. By constructing a discrete piecewise Lyapunov function in each maximal overlapped-rule group, the systematic design of the fuzzy robust H∞ controller is studied through the parallel distributed compensation control scheme, and a new sufficient condition to check the robust asymptotic stabilization of the closed-loop discrete uncertain T–S fuzzy system is proposed and confirmed. This sufficient condition requires only finding common matrices in each maximal overlapped-rule group. Compared with the common Lyapunov function approach and the fuzzy Lyapunov function approach, the proposed sufficient condition can not only overcome the defect of finding common matrices in the whole feasible region but also significantly reduce the number of linear matrix inequalities to be solved. Therefore, the proposed condition is less conservative and difficult than the other two approaches. Finally, the simulation results for a class of two-echelon uncertain nonlinear supply chain systems show the effectiveness of the proposed approach.

LMI-based Relaxed Quadratic Stability Criterion for Discrete Takagi-Sugeno Fuzzy Systems

Abstract Many stability criteria have been proposed based on the single Lyapunov function and the fuzzy Lyapunov function. But there is still a room to reduce the conservatism of the existing stability criteria. This paper studies the relaxed problem of the quadratic stability criterion for discrete Takagi-Sugeno fuzzy systems. Based on the definitions of the efficient maximal overlapped-rules group (EMORG) and the piecewise fuzzy Lyapunov function, a LMI-based sufficient criterion of the asymptotical stability is proposed to guarantee quadratic stability of the discrete open-loop Takagi-Sugeno fuzzy systems globally. Finally, the simulation result of an example shows the effectiveness of the proposed stability criterion.

Controller design of uncertain nonlinear systems based on T-S fuzzy model

A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group (EMORG) is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.

Stability analysis and systematic design of Takagi–Sugeno fuzzy control systems

The stability analysis and systematic design techniques of Takagi–Sugeno (T–S) fuzzy control systems are discussed in this paper. In order to make good use of the structural information in rule base to decrease the conservatism of the stability analysis, the standard fuzzy partition of the input variables of fuzzy control systems is well defined. Based on the property analysis of fuzzy control systems with SFP inputs, the stability of both the input-free T–S fuzzy systems and the closed-loop T–S fuzzy control systems are studied in detail with the extended Lyapunov theory, and two theorems to check the stability of T–S fuzzy control systems are proposed. These methods, which only require to find a common positive-definite symmetric matrix in each maximal overlapped-rules group, can reduce the conservatism and difficulty of the former stability analysis approaches. Using the method of parallel distributed compensation, a systematic design approach of T–S fuzzy control systems is presented. The simulation results of three examples show that these methods are effective.