This paper propose the two steps methed that adjusts optimally the input coefficient matrix in accordance with relative increments, this method is more retional than that in accordance with absolute increments.

The Lie symmetry of the system is discussed;the perturbation of symmetries under the infinitesimal transformations is studied;s-order adiabatic invariants are constructed;and the existence conditions and forms of adiabatic invariants is presented.

Perturbation to the symmetries of the systems under infinitesimal transformations, s-order adiabatic invariants, existence conditions an.

Perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical system in phase place;

Lie symmetries and adiabatic invariants for holonomic systems in event space;

Perturbation of Lie symmetries and a type of generalized Hojman adiabatic invariants for variable mass systems with unilateral holonomic constraints;