In this paper we investigate the problem of autonomous task assignment for a class of uncertain systems described by dynamic weighted bipartite graphs. Specifically, we consider the optimal assignment problem for this class of system. First, we present necessary and sufficient conditions for the existence of a perfect matching in a given bipartite graph. Next, we present an algorithm to expand the original graph to a virtual graph that guarantees the existence of a perfect matching. These results are then used to solve the optimal assignment problem for dynamic weighted bipartite graphs. Finally, we apply this algorithm to a group of low-earth orbit satellites that have the task of tracking multiple ground targets simultaneously.