A new approach to fuzzy estimation of Takagi–Sugeno model and its applications to optimal control for nonlinear systems

Abstract

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

New incremental Takagi–Sugeno state model for optimal control of multivariable nonlinear time delay systems

“…The formulation of the discrete state allows the inclusion of delays within the state itself. In this work, we show that the control action in an incremental state form is equivalent to introducing an integral action, thereby cancelling the steady state errors (Al-Hadithi et al, 2012;Jiménez et al, 2014). Most recent works devoted to the modeling and control of delayed T-S fuzzy models are based on system states or input/output models rather than the incremental states as we propose in this work.…”

“…The idea is based on estimating the nonlinear system parameters minimizing a quadratic performance index. Al-Hadithi et al (2012) proposed the following identification method to improve T-S identification method.…”

“…New and efficient approaches are presented to improve the local and global estimation of T-S model (Al-Hadithi et al, 2012, 2013. The aim is to obtain high function approximation accuracy and fast convergence.…”

Variable Structure Control with chattering elimination and guaranteed stability for a generalized T-S model

“…where Ifs(x) < 0 thena = K lfs(x) = 0 thena = 0 (8) Ifs(x) > 0 thena = -K Differentiating (5) and substituting (1) in it, we get:…”

“…The authors developed an approach [ 1 ] which can be considered as a generalized version of T-S method with optimized performance in approximating (locally and globally) nonlinear functions. It is a simple approach with few computational effort, based on the well known parameters weighting method for tuning T-S parameters to improve the choice of the performance index and minimize it.…”