LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation

Abstract

In this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear matrix inequality method. The conditions of linear matrix inequality guarantee the asymptotical stability of the system based on the Lyapunov theorem. The stabilizer and observer parameters are obtained using linear matrix inequalities, which make the state errors converge to the origin. The effects of the nonlinear Lipschitz perturbation and external disturbances on the system stability are then reduced. Moreover, the stabilizer and observer design techniques are investigated for the nonlinear systems with an output nonlinear function. The main advantages of the suggested approach are the convergence of estimation errors to zero, the Lyapunov stability of the closed-loop system and the elimination of the effects of perturbation and nonlinearities. Furthermore, numerical examples are used to illustrate the accuracy and reliability of the proposed approaches.

A Robust Iterative Learning Control for Continuous-Time Nonlinear Systems With Disturbances

“…This variation causes a failure of the convergence condition (5), and no conclusions on the convergence of the iterative method can be drawn. However, this simulation shows that using the gain (35), we can guarantee the convergence thanks to (7).…”

“…The disturbances are due to model uncertainties and a change in the relative degree, namely d pt (t). • D -Noise: we employ (35), and, in addition to the issues of the D -Model case, we inject Gaussian noise into the system simulating the presence of time-nonrepetitive disturbances rty j (t). The mean value of the Gaussian noise is equal to 0, the standard deviation equal to 10 −3 on the position measurements, and 10 −5 on the velocity measurements.…”

“…• ND: we use the nominal model in (24), where D(x j ) is computed as (33). • D -Model: we design the learning gain using (35). The disturbances are due to model uncertainties, i.e., d px (t).…”

Analysis and Research on Nonlinear Complex Function Approximation Problem Based on Deep Learning

“…Huang Wei, Dai Jianhua, etc. applied the nonlinear function to GDP prediction and achieved good results, which also laid the foundation for this study [9][10][11][12][13]. It provides a reference for the application of the traditional shallow mathematical model for the analysis of complex nonlinear problems.…”

Improved Nonlinear Extended State Observer-Based Sliding-Mode Rotary Control for the Rotation System of a Hydraulic Roofbolter

“…To the best of our knowledge, control methods based on a disturbance observer can effectively enhance the anti-disturbance ability and improve the control performance of systems [ 16 ]. Based on this, in order to better suppress chattering, disturbance observer-based sliding-mode control has received extensive attention.…”