Abstract
The paper is concerned with the design of H∞ state estimator of a dynamical system based on fuzzy modeling. At first, a universal linear model is considered with some unknown variables. Since the variables are not time invariant in modeling of a real nonlinear system so they are modeled by fuzzy approximates with some free parameters. The system states constitute input variables of the fuzzy system. Then, a stable state and parameter estimator based on H∞ criterion and some circumstances is proposed. By assuming some conditions, it will be proved that the parameter estimator is just modified normalized least mean squares (NLMS) algorithm which follows H∞ optimality. It is used for estimating the fuzzy model parameters. In this way, it reduces required tuning parameters of the filter. The proposed model can be used in signal processing such as time series and speech processing or in nonlinear circuit modeling. In this paper, suggested algorithm is implemented on a practical data gathered from a real nonlinear system. The results show stability, good performance, fast convergence time, and robustness to far initial conditions of the suggested estimator. For comparison, the proposed method is compared with the one in which the identified free parameters are not adjusting during estimation process.
Get full access to this article
View all access options for this article.