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A Structured Linear Quadratic Controller for Transportation Problems

We study a linear quadratic control problem for transportation optimization on a directed line graph. We show that the solution to the Riccati equation associated with this problem is highly structured. The feedback law is almost upper triangular, and the synthesis of the feedback law is given by a recursion, making it scalable. The structure of the feedback law also allows for an efficient realization of the controller using a local communication scheme.