Synthesis methods for controlling multiscale processes with predictive models with incomplete information

Methods for the synthesis of control of multi-scale processes with predictive models for linear and non-linear systems, as well as with various restrictions on the target functional of the system, including the case with terminal restrictions, are considered. This problem is relevant in the modeling and control of technological processes for growing nanoscale structures. A description is given of a control scheme in which the current control action is obtained by solving at each instant of the sample the optimal control problem with a finite horizon without feedback and using the current state of the object as the initial state. An optimization problem is described that gives an optimal control sequence when the control obtained for the first step of the subsequent sequence is applied to the object. The main differences from traditional control schemes that use a pre-computed control law are described.