On the polyhedral method of solving problems of control strategy synthesis

Abstract

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. Nonlinear systems of ordinary differential equations describing the mentioned polyhedral solvability tubes are presented. We propose new control strategies, which can be calculated by explicit formulas based on the mentioned tubes. In addition, we consider similar synthesis problems for multistage systems.