Robust fuzzy control for discrete perturbed time-delay affine Takagi-Sugeno fuzzy models

Abstract

The purpose of this paper is to study the stability analysis and controller synthesis principles of Discrete Perturbed Time-Delay Affine (DPTDA) Takagi-Sugeno (T-S) fuzzy models. In general, the T-S fuzzy model is a weighted sum of some linear subsystems via fuzzy membership functions. This paper considers fuzzy rules include both linear nominal parts and uncertain parameters in the time-delay affine T-S fuzzy model. For DPTDA T-S fuzzy models, the T-S fuzzy control scheme is used to confront the H ∞ performance constraints. Some sufficient conditions are derived on robust H ∞ disturbance attenuation in which both robust stability and a prescribed performance are required to be achieved. In order to find suitable fuzzy controllers, the Iterative Linear Matrix Inequality (ILMI) algorithm is employed to solve these sufficient conditions. At last, a numerical simulation for the nonlinear truck-trailer system is given to show the applications of the present design approach.

Robust fuzzy controller design for dynamic positioning system of ships

“…The purpose of robust optimization is to attain the minimum σ 2 in (29) so as to acquire maximum elimination of the effect of disturbance d E (t). For (10), the design problem is how to stipulate a stabilizable fuzzy controller in (19) so as to minimize σ 2 subject to the constraint in (29).…”

“…The aim is to specify the fuzzy linear control law presented in (19) for the system in given in (21) with the guaranteed H ∞ control performance in (29). Hence, we proceed as follows: let a Lyapunov candidate function be chosen as…”

“…In recent years, there has been a fast growth of interest in fuzzy control design of nonlinear systems and there have been successful results. For instance, a robust fuzzy controller for the discrete perturbed time delay affine T-S fuzzy model has been developed [29]. The purpose of the study given in [29] was to achieve the H ∞ performance constraints and cope with the nastiest case effects of the disturbances.…”

“…For instance, a robust fuzzy controller for the discrete perturbed time delay affine T-S fuzzy model has been developed [29]. The purpose of the study given in [29] was to achieve the H ∞ performance constraints and cope with the nastiest case effects of the disturbances. More works related to robust fuzzy have been given in [27][28][29][30][31][32][33][34][35][37][38].…”

“…Some of these literatures have no direct comparison to the proposed work but show the richness of fuzzy control designs. The performances of some literatures proposed in [28][29][30][31][32][33][34] are discussed in section four. Thus, this paper proposes a linear fuzzy controller design based on the nonlinear H ∞ control scheme for the control of dynamic positioning of the system of ships.…”