Abstract
This paper presents a novel optimal control problem, referred to as distributed optimal control, that is applicable to multiscale dynamical systems comprised of numerous interacting agents. The system performance is represented by an integral cost function of the macroscopic state that is optimized subject to a hyperbolic partial differential equation known as the advection equation. The microscopic control laws are derived from the optimal macroscopic description using a potential function approach. The optimality conditions of the distributed optimal control problem are first derived analytically and, then, demonstrated numerically through a multi-agent trajectory optimization problem.
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