Mathematical models and control for systems with segregation

We consider mathematical models and optimal control problems for systems that consist of a large number of uncontrolled aggregates and an environment interacting with them. The evolution of each aggregate is described by an ordinary differential equation with a random parameter; the evolution of the environment is defined by the averaged interaction with aggregates and the values of control parameters. We obtain optimality conditions and develop an approach to the calculation of the distribution densities of the residence time of aggregates in the system.