Based on the generalized Huygens-Fresnel diffraction integral, the analytic propagation expressions for Lorentz beams passing through first-order axisymmetric optical system are derived.

The specific distribution function of a relativistic kinetic system is given and its Lorentz scalar property is proved. A relativistic generalized Liouville equation is established.

Finally, Lorentz chaotic system is taken as an example to demonstrate the validity of the proposed controller.