Minimax terminal state estimation for linear plants with unknown forcing functions

An admissible minimax estimate for the terminal state of a linear discrete system with an unknown control sequence is derived with respect to a generalized quadratic loss function. This loss function is quadratic in both the terminal state estimation error and the unknown control sequence. The estimate is derived using the method of least favourable prior distributions. It is linear, and the least favourable prior distribution for the unknown control sequence is normal with zero mean. The covariance of this least favourable normal distribution is determined by the solution of a certain non-linear algebraic matrix equation. This minimax estimation problem is shown to be equivalent to a constrained minimization problem. Further, sufficient conditions are developed under which this minimax terminal state estimate can be realized as a discrete time Kalinau filter.