Motion of multiple agents with identical non-linear dynamics is controlled to change density of the agents from the initial to the final density. A first control problem is formulated for optimizing a control cost of changing density of the agents from the initial density to the final density subject to dynamics of the agents in a density space. The first control problem, which is a non-linear non-convex problem over a multi-agent control and a density of the agents, is transformed into a second control problem over the density of the agents and a product of the multi-agent control and the density of the agents. The second control problem is a non-linear convex problem that is solved to produce the control input for each section of the state space. A motion of each agent is controlled according to a control input corresponding to its section of the state space.