On the polyhedral method of solving problems of control strategy synthesis

We consider control synthesis problems for linear and bilinear differential systems. Two types of problems are studied: when controls are additive and when they enter the matrix of the system. For both types we consider cases without uncertainty and cases with uncertainty, including additive parallelotope-valued uncertainties and interval uncertainties in the coefficients of the system. We continue to develop the methods of “polyhedral” synthesis of controls with the use of polyhedral (parallelotope-valued) solvability tubes. We propose new control strategies, which can be calculated by explicit formulas based on the mentioned tubes, and consider similar synthesis problems for multistep systems.