Mathematical modelling and control of the evolution of dynamic systems interacting with medium

The article proposes a new method of mathematical modeling evolutional systems interacting with medium. A cutting process or tribo-space formed in the contact area of two conjugate mechanical subsystems is considered as medium. The features of the medium depend not only on state coordinates of systems but also on trajectories. It is obtained that the parameters of the medium are performed as integral operators of equations like Volterra equations of 2$^{nd}$ type. The problems of control of evolutional systems are being analyzed.Keywords: Evolutional system, interact, medium.