Distributed Optimal Control of Multiscale Dynamical Systems: A Tutorial

Many complex systems, ranging from renewable resources [1] to very-large-scale robotic systems (VLRS) [2], can be described as multiscale dynamical systems comprising many interactive agents. In recent years, significant progress has been made in the formation control and stability analysis of teams of agents, such as robots, or autonomous vehicles. In these systems, the mutual goals of the agents are, for example, to maintain a desired configuration, such as a triangle or a star formation, or to perform a desired behavior, such as translating as a group (schooling) or maintaining the center of mass of the group (flocking) [2]-[7]. While this literature has successfully illustrated that the behavior of large networks of interacting agents can be conveniently described and controlled by density functions, it has yet to provide an approach for optimizing the agent density functions such that their mutual goals are optimized.