The application of the variational principle in the constrained control system

The regular equations on the constraint variables are established for LQ and non-linear control problems in this paper,then the extreme-value principles of con-straint variables are discussed for the equality and unequality constraint cases respec-tively. At last, the given example verifies the conclusion of this paper.The work in this paper will lay the foundation for the further study about the constrained LQ and non-linear control systems.