Simultaneous control and estimation of linear stochastic systems with unknown parameters of disturbances

In the present paper methods of the decision theory are applied to determine minimax policies of simultaneous control and estimation for stochastic system (1). There are solved the following cases:

a)when disturbances of the system have the binomial distribution with unknown parameter

b)when disturbances of the system have distribution belonging to an exponential family dependent on natural unknown parameter and the class of prior distributions of parameter is restricted by fixing the second moment

In both cases open analytical forms of minimax policies are given