Multi-Agent Control System and Method

A method for controlling a motion of multiple agents with identical non-linear dynamics, comprising:

• receiving data indicative of at least one or combination of an initial density of the agents in a state space and a final density of the agents in the state space at a given time, wherein the state space is partitioned into a set of sections, such that a density of a section of the state space is proportional to a number of agents having states within the section of the state space;
• formulating a first control problem 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, wherein the first control problem is a non-linear non-convex control problem over a multi-agent control and a density of the agents, wherein the multi-agent control is a function parameterized on the set of sections of the state space defining a control input for each section of the state space;
• transforming the first control problem into a second control problem, wherein the second control problem is a non-linear convex problem over the density of the agents and a product of the multi-agent control and the density of the agents;
• solving the second control problem to produce the control input for each section of the state space;
• and
• controlling a motion of each agent according to a control input corresponding to its section of the state space, wherein at least some steps of the method are performed using a processor.

A non-transitory computer readable storage medium embodied thereon a program executable by a processor for performing a method, the method comprising:

• receiving data indicative of at least one or combination of an initial density of the agents in a state space and a final density of the agents in the state space at a given time, wherein the state space is partitioned into a set of sections, such that a density of a section of the state space is proportional to a number of agents having states within the section of the state space;
• formulating a first control problem 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, wherein the first control problem is a non-linear non-convex control problem over a multi-agent control and a density of the agents, wherein the multi-agent control is a function parameterized on the set of sections of the state space defining a control input for each section of the state space;
• transforming the first control problem into a second control problem, wherein the second control problem is a non-linear convex problem over the density of the agents and a product of the multi-agent control and the density of the agents;
• solving the second control problem to produce the control input for each section of the state space;
• and
• controlling a motion of each agent according to a control input corresponding to its section of the state space.