Kalman duality principle for a class of ill-posed minimax control problems with linear differential- algebraic constraints

In this paper we present Kalman duality principle for a class of linear Differential-Algebraic Equations (DAE) with arbitrary index and timevarying coefficients. We apply it to an ill-posed minimax control problem with DAE constraint and derive a corresponding dual control problem. It turns out that the dual problem is ill-posed as well and so classical optimality conditions are not applicable in the general case. We construct a minimizing sequence ûε for the dual problem applying Tikhonov method. Finally we represent ûε in the feedback form using Riccati equation on a subspace which corresponds to the differential part of the DAE. Mathematics Subject Classification (2000). Primary 34K32 49N30 49N45x; Secondary 93E11 93E10 60G35.