Date of this Version
United States Patent Grover et al. Patent No . : US 10 , 409 , 230 B2
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 trans formed 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 .