Analytical reachability results for a class of nonlinear systems with ellipsoidal initial sets

Existing reachability theory and optimal control theory are applied to a class of nonlinear systems with ellipsoidal initial reachability sets, reflecting information typically provided by industry-standard optimal estimation methods. Analytical expressions for position-and velocity-extrema are developed, yielding necessary conditions for reachability as well as tools for significant reduction in reachability computation requirements. Similar relations for position and velocity reachability set surface computation are also developed and the computation implications discussed. Several examples are worked to illustrate results, and finally directions for future work are discussed.