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 time-varying 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 <##> } } u }^<!-- ^ --> } ε<!-- ?? --> $ /hat{u}{sub {/varepsilon}} $ u-hat {sub ε} </##> for the dual problem applying Tikhonov method. Finally we represent <##> } } u }^<!-- ^ --> } ε<!-- ?? --> $ /hat{u}{sub {/varepsilon}} $ u-hat {sub ε} </##> in the feedback form using Riccati equation on a subspace which corresponds to the differential part of the DAE.