The Dynamic Feedback Matrix Control for Multidimensional Chaotic Systems

Abstract

Multidimensional chaotic systems are difficult to control because of their nonlinearity and coupling relationship among state variables. We present the error feedback matrix for nonlinear systems, which contains coupling information of state variables and updates online according to the gradient descent method. The error feedback matrix is similar to the state feedback matrix for linear systems, however, the former is time-varying and converges to a constant matrix. Using the coupling relationship, we give a simple controller only by a few elements of the matrix and present whole matrix control and partial matrix control. Finally, we apply these schemes to a three-dimensional Henon system and make mathematical analysis and simulation experiments, which verify the effectiveness of the proposed controllers. in Wiley Online Library 297-303 820 Fig. 2. The Henon system is driven to (0.8861, 0.8861, 0.8861), starting from (1,0,−1) with η = 0.2. Here, red lines denote xk(1) and uk(1), green lines denote xk(2) and uk (2), and blue lines denote xk(3) and uk(3). This notation remains consistent in the following.

Controlling Chaos and Neimark–Sacker Bifurcation in a Host–Parasitoid Model

“…For similar types of investigations we refer to [1,[32][33][34][35][36][37][38][39][40][41] for controlling chaos in discrete-time population models. For some other applications related to chaos control, see also [51][52][53][54][55][56][57][58][59][60][61][62].…”