On polyhedral estimates for reachable sets of differential systems with bilinear uncertainty

Systems of nonlinear ordinary differential equations describing the dynamics of internal parallelotope-valued estimates for reachable sets of differential systems with bilinear uncertainty are derived. The existence and uniqueness of solutions are proved at least on some subinterval of the time interval under consideration and, in the case of single-valued additive terms in the right-hand sides of the original equations, on the whole interval. Two types of differential inclusions that guarantee the extension of estimates to the whole interval are obtained. The second of these inclusions produces nondegenerate parallelepiped-valued estimates. Some conditions are specified under which the proposed estimates are most efficient. Differential equations for external parallelepiped-valued estimates of reachable sets were obtained earlier. Here, for unification, they are given in the form of equations describing the dynamics of the centers and matrices of parallelotopes. Results of numerical simulation are presented.