New methods for the estimation of Takagi–Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T‐S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T‐S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T‐S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T‐S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T‐S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T‐S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use. Copyright © 2011 John Wiley & Sons, Ltd.     

Design of robust quadratic‐optimal controllers for uncertain singular systems using orthogonal function approach and genetic algorithm

This paper discusses the robust‐optimal state feedback controller design problems of linear singular systems under the structured (elemental) parameter uncertainties by using the orthogonal function approach (OFA) and the hybrid Taguchi genetic algorithm (HTGA). A sufficient condition is proposed to ensure that the linear singular systems with the structured parameter uncertainties are regular, impulse free, and asymptotically stable. Based on the OFA, an algorithm only involving algebraic computation is derived in this paper and then is integrated with the HTGA to design the robust‐optimal state feedback controller of linear uncertain singular systems subject to robust stability constraint and the minimization of a quadratic performance index. A design example of a two degree of freedom mass–spring–damper system is given to demonstrate the applicability of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive fault tolerant control design for Takagi–Sugeno fuzzy systems with interval time‐varying delay

This paper deals with the problem of fault‐tolerant control (FTC) of continuous‐time Takagi–Sugeno fuzzy systems with interval time‐varying delay by using adaptive observer. Through constructing an appropriate type of Lyapunov function, a delay‐dependent criterion is established to reduce the conservatism of designing an active FTC (AFTC). In comparison with the existing techniques in the literature, the proposed approach simplifies the design of an AFTC and gives in only one step of the estimate of state vector, the estimate of actuator fault and the controller gains. Some simulation examples are included to demonstrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Design of ℋ︁∞ fuzzy controllers for nonlinear systems with random data dropouts

The problem of ??_∞ control of nonlinear networked control systems subject to random data dropout is concerned in this paper. The random data dropout, because of the limited bandwidth of the network channels, could exist in the communication channels both from the sensor to the controller and from the controller to the actuator simultaneously. The nonlinear plant is represented by the well‐known Takagi–Sugeno fuzzy model and the random data dropout is expressed by the Bernoulli random binary distribution. In the presence of random data dropout, two control schemes, state feedback and static output feedback, are proposed to design ??_∞ controllers such that the closed‐loop system is stochastically stable and preserves a guaranteed ??_∞ performance. The addressed controller design problem is transformed to an auxiliary convex optimization problem, which can be solved by a linear matrix inequality approach. Three examples are provided to illustrate the applicability and less conservativeness of the developed theoretical results. It is easy to see that our approach is simple but our results are much less conservative than the recently published results. Copyright © 2010 John Wiley & Sons, Ltd.