Weak pullback attractors of setvalued processes

Weak pullback attractors are defined for nonautonomous setvalued processes and their existence and upper semicontinuous convergence under perturbation is established. Unlike strong pullback attractors, invariance and pullback attraction here are required only for at least one trajectory rather than all trajectories at each starting point. The concept is useful in, for example, continuous time control systems and is related to that of viability.