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This paper asks a new question: how can we control the collective behavior of self-organized multi-agent systems? We try to answer the question by proposing a new notion called ‘Soft Control’, which keeps the local rule of the existing agents in the system. We show the feasibility of soft control by a case study. Consider the simple but typical distributed multi-agent model proposed by Vicsek et al. for flocking of birds: each agent moves with the same speed but with different headings which are updated using a local rule based on the average of its own heading and the headings of its neighbors. Most studies of this model are about the self-organized collective behavior, such as synchronization of headings. We want to intervene in the collective behavior (headings) of the group by soft control. A specified method is to add a special agent, called a ‘Shill’, which can be controlled by us but is treated as an ordinary agent by other agents. We construct a control law for the shill so that it can synchronize the whole group to an objective heading. This control law is proved to be effective analytically and numerically. Note that soft control} is different from the approach of distributed control}. It is a natural way to intervene in the distributed systems. It may bring out many interesting issues and challenges on the control of complex systems.

Soft Control on Collective Behavior of a Group of Autonomous Agents By a Shill Agent