In this paper, we focus on ellipsoidal estimates of reachable sets for discrete-time nonlinear dynamical systems based on ellipsoidal set-membership techniques. To this end, we implement a set-membership filter that utilizes state dependent coefficient parameterization of the nonlinear dynamics. The set-membership filter has a correction-prediction form similar to the Kalman Filter and generates optimal (minimum 'size' based on the trace criteria) ellipsoids at the correction and prediction steps, containing the true state of the system. At every time step, the optimal prediction ellipsoid provides an estimate of the reachable set. Also, information from the filter is utilized to formulate a family of ellipsoids containing the reachable set at each time step. The minimum 'size' ellipsoid (based on the trace criteria or the log-determinant criteria) of this family is identified as another ellipsoidal estimate of the reachable set. Simulation examples are included to illustrate results corresponding to the two estimates.
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