Description of Dynamics of Ellipsoidal Estimates of Reachable Sets of Nonlinear Control Systems with Bilinear Uncertainty

Abstract

The state estimation problems for control systems with unknown but bounded uncertainties with a set-membership description of uncertain parameters and functions are studied. The modified state estimation approaches based on special structure of nonlinearity and uncertainty that are simultaneously present in the control system are developed. The studies are motivated by numerous modeling problems for dynamical systems with uncertainty and nonlinearity arising in different fields such as physical engineering problems, economical modeling, ecological problems. This investigation continues previous researches and a more complicated case is considered here, when the dynamical equations of control system contain two types of nonlinearities, one of which is of quadratic type and another one contains uncertain matrix parameters. Such models may arise in applications related, in particular, to satellite control problems with nonlinearity and disturbances in the model description. The main new results consist in deriving the dynamical equations for the ellipsoidal estimates of reachable sets of the control system under study. Related numerical algorithms and simulation results are also given.