Abstract
The paper is devoted to the construction of ellipsoidal estimates for reachable sets of the nonlinear control system with uncertainty in the initial data. The initial states are taken to be unknown but bounded with given bounds. The system nonlinearity has a quadratic structure. Basing on the results of ellipsoidal calculus developed earlier for linear uncertain system we present here the state estimation algorithms which allows to construct the external ellipsoidal estimates of reachable sets. We also consider a nonlinear system of Lotka-Volterra type and propose a method for constructing an ellipsoidal estimate of the reachable sets for this system. This method allows to effectively construct an estimate of the reachable set without using resource-intensive calculations. A numerical simulation is performed.
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