Estimating reachable sets of control systems with uncertainty on initial data and with nonlinearity of a special kind

The problem of estimating the trajectory tubes of nonlinear control dynamical system with uncertainty in the initial data is studied. It is assumed that the dynamic system has a special structure in which the nonlinear terms are defined by quadratic forms on state coordinates and the values of uncertain initial states and admissible controls are constrained by ellipsoidal restrictions. We assume also that the coefficients of the matrix in linear terms of system velocities also are not exactly known, but belong to the given compact set in the corresponding space, that is the system contains also bilinear terms. The paper presents approaches and algorithms allowing to find external ellipsoidal estimates of reachable sets of nonlinear control system with combined bilinear and quadratic nonlinearities.