Output Regulation of the Lu-Chen Attractor

Output regulation of nonlinear control systems is a central problem in the nonlinear control theory. Basically, in the output regulation problem, we aim to regulate a fixed linear or nonlinear plant so that its output tracks the reference signals produced by some external input generator. In this paper, we investigate the problem of regulating the output of the Lu-Chen chaotic attractor (2002), which is one of the recently discovered three-dimensional chaotic attractors. Lu-Chen chaotic attractor has many interesting complex dynamical behaviours and it has potential applications in secure communication. In this paper, we derive explicit state feedback control laws to regulate the output of the Lu-Chen chaotic attractor so as to track constant reference signals. The control laws are derived using the regulator equations of Byrnes and Isidori (1990), who have solved the output regulation of nonlinear control systems involving neutrally stable exosystem dynamics. Numerical simulations are also illustrated in detail to illustrate and validate the regulation schemes derived in this paper for the Lu-Chen chaotic attractor.