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Optimal control of large particle systems with collective dynamics by fewagents is a subject of high practical importance (e.g. in evacuation dynamics),but still limited mathematical basis. In particular the transition fromdiscrete optimal control to a continuum setting as the number of particlestends to infinity is by far not fully understood. In this paper we contributeto this issue by studying a canonical model of controlling an interactingparticle system into a certain spatial region by repulsive forces from fewexternal agents, which might be interpreted as shepherd dogs leading sheep totheir home.  We discuss the appropriate modelling of such a problem and the associatedoptimality systems, providing some connections between the Lagrange multipliersin the discrete and continuum setting. As control strategies we investigate anInstantaneous Control and a global Optimal Control approach.  The solutions of a family of control problems for the particle system withexternal agents are numerically compared to the mean-field controls as thenumber of particles tends to infinity. In both cases, this leads to a highdimensional phase space requiring tailored optimization strategies. All controlproblems arising are solved using adjoint information to compute the descentdirections. The numerical results indicate the convergence of controls for bothoptimization strategies.

Controlling a self-organizing system of individuals guided by a few external agents -- particle description and mean-field limit