The treatment of problems in control and observation under various types of uncertainty or partial information is often reduced to the description of controlled set-valued dynamics, especially for ellipsoidal-valued tubes. This paper indicates the statement and solutions of target control problems for ellipsoidal-valued motions which have to evolve while avoiding external obstacles and also observing an internal bound that excludes degeneracy of the tubes throughout the motion. The techniques rely on Hamiltonian methods for matrix differential equations. The motivations for such problems include those of reachability, guaranteed state estimation, output feedback control as well as coordinated multiagent team control and distributed observation.