Precise computation for control law of singular control system

The singular control is a hot problem in control region, especially for complex control system. A discreted linear quadratic control problem was considered, in which the singularity of weighting matrix R appears. Based on the substructural condensation algorithm in computational structural mechanics and precise integration method, the precise computational method for control law of the singular control system was given. On the basis of the elimination of singularity for the system, the condensation formulas of time-interval were given by using the definition of time-interval mixed energy and generalized variational principle. By introducing the 2^N precise computational algorithm, the solved method for the algebraic Riccati equation of the singular control system was obtained. For showing the characteristics of the singular control system better, the control law was divided into first and second control laws. The effectiveness of the method is shown in a numerical example.