Singular optimal control for MIMO systems with persistent disturbances

Considering the persistent disturbances and the restraint of control variables in multivariable time-varying systems, an approximate singular optimal control method is presented, which makes use of a non-singular control problem instead of singular one. Firstly, this method presents the sufficient and necessary condition for the existent of non-singular optimal control law. Then the approximate optimal control law is obtained by optimizing according to the restraint of control variables, which improves the singular control method. The simulation result demonstrates its effectiveness.