Continuous-discrete dynamic models

We consider dynamic models with an aftereffect in the form of functional differential equations with continuous and discrete time. We formulate a general control problem with respect to a given system of target functionals and a brief summary of known results on solvability of this problem under polyhedral point control constraints. In concluding section we present results on estimating the set of attainability under integral restrictions for the control. The proposed version of the synthesis of continuous and discrete systems is based on the systematic use of the theory abstract functional differential equation and has certain advantages in the study of systems and processes with aftereffect. Continuous-discrete functional-differential models allow us to take into consideration the aftereffects when modeling, including cases of complete memory, and effects arising when impulse perturbations (shocks) are taken into consideration and they are leading to jump changes in the phase state by components with continuous time.