Feedback control for linear systems that are not solved with respect to the derivative (Q759709)

The paper considers the optimal feedback problem for the system \((Dx)_ t=Ax+Bu\), \(Dx(t_ 0)=x^ 0\), where the matrix D is not necessarily invertible. The standard strictly convex quadratic functional is considered. It is proved that the optimal control can be determined in a feedback form by the solution of a certain matrix differential equation that corresponds to a Riccati equation which is not solved with respect to the derivative. The solvability of this equation is discussed.