  The chemical self-assembly has been considered as one of most important
scientific problems in the 21th Century; however, since the process of
self-assembly is very complex, there is few mathematic theory for it currently.
This paper provides a novel multi-agent model for chemical self-assembly, where
the interaction between agents adopts the classic Lennard-Jones potential.
Under this model, we propose an optimal problem by taking the temperature as
the control input, and choosing the internal energy as the optimal object. A
numerical solution for our optimal problem is also developed. Simulations show
that our control scheme can improve the product of self-assembly. Further more,
we give a strict analysis for the self-assembly model without noise, which
corresponds to an attraction-repulsion multi-agent system, and prove it
converges to a stable configuration eventually.
