Parameterization technique for solving variational formulation of index three linear time-varying singular control systems

Abstract

This paper deals with finding an approximate solution to an index three time-varying linear differential algebraic control equations based on the theory of variational formulation. The critical points of the formulated variational functional subject to the differential- algebraic equation with the class of consistent initial conditions are shown to be the solution of the proposed index-three DAEs with control problem (singular control systems) and vise- versa. The given variational problem is also transformed from indirect method into direct method using generalized Ritz bases technique. From the numerical illustrations results, the efficiency and very good accuracy as well as the simplicity of the present approach are obtained.