Classical control theory does not scale well for large systems such as traffic networks.
However, many of these applications can be handled efficiently using the concept of positive system, exploiting that the set of positive states is left invariant by the dynamics. Positive systems, and the nonlinear counterpart monotone systems, are useful models in many branches of science and engineering, including traffic networks.
In this presentation, we will highlight several fundamental advantages of positive control systems: Verification and synthesis can be done with a complexity that scales linearly with the number of states and interconnections. Distributed controllers can be designed by convex optimization. Lyapunov functions and storage functions for nonlinear monotone systems can be built from scalar functions of the states, with dramatic simplifications as a result. The theory will be illustrated by applications in traffic networks.
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