State Observer Based Dynamic Fuzzy Logic System for a Class of SISO Nonlinear Systems

Abstract

This paper presents an observer based dynamic fuzzy logic system (DFLS) scheme for a class of unknown single-input single-output (SISO) nonlinear dynamic systems with external disturbances. The proposed approach does not need the availability of the state variables. Within this scheme, the DFLS is employed to identify the unknown nonlinear dynamic system. The control law and parameter adaptation laws of the DFLS are derived based on Lyapunov synthesis approach. The control law is robustfied in H∞ sense to attenuate external disturbance, model uncertainties, and fuzzy approximation errors. It is shown that under appropriate assumptions, it guarantees the boundedness of all the signals in the closed-loop system and the asymptotic convergence to zero of tracking errors. The proposed method is applied to an inverted pendulum system to verify the effectiveness of the proposed algorithms.

Improved Discrete Techniques of Time‐Delay and Order Estimation for Large‐Scale Interconnected Nonlinear Systems

“…As a result, we can conclude that the model order is equal to 2 for each interconnected subsystem . Therefore, these results indicate the performance and the efficiency of the developed algorithm (11) for the order estimate of a large-scale interconnected nonlinear system described by the Hammerstein model (1).…”

“…In the literature, several presentations are used to describe the dynamics of this class of systems. We can cite input-output discrete models [11], continuous statespace models [1,2], and block-oriented mathematical models [10,[12][13][14]. In this framework, we consider the class of largescale systems which consist of several interconnected Hammerstein subsystems operating in a stochastic environment with unknown time-varying parameters and described by the following dynamic equation:…”

“…In this section, we are proposed to formulate the structural estimation problem for the class of large-scale interconnected nonlinear stochastic systems described by the mathematical model (1). The formulation of this problem can be classified into two subsections.…”

“…In [15], the developed DR technique is based on the product-moment matrix containing several input-output signals measurements from the system. In this part, the purpose is to extend this approach in order to estimate the order of large-scale interconnected nonlinear systems, which is described by the discrete-time mathematical model (1).…”

“…These works preoccupied more particularly the large-scale systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14], the nonlinear systems , and the nonstationary systems [12][13][14]. The class of large-scale systems can be found in different fields as transportation processes, power processes, communication networks, space structures, and others.…”