Output Regulation of the Simplified Lorenz Chaotic System

This paper investigates the problem of designing feedback controllers for regulating the output of the simplified Lorenz system, which is a novel chaotic system recently discovered by K.H. Sun and J.C. Sprott (2009). The simplified Lorenz chaotic system is a three-dimensional chaotic system with one bifurcation parameter and it includes the Lorenz attractor (1963) as a special case. In this paper, state feedback control laws to regulate the output of the simplified Lorenz chaotic system have been derived so as to track the constant reference signals. The control laws are derived using the regulator equations of C.I. Byrnes and A. Isidori (1990), who solved the problem of output regulation of nonlinear systems involving neutrally stable exosystem dynamics. Numerical simulations are shown to illustrate the results.