A Decentralized Optimal Feedback Flow Control Approach for Transport Networks

Finite-time optimal feedback control for flow networks under information constraints is studied. By utilizing the framework of multi-parametric linear programming, it is demonstrated that when cost/constraints can be modeled or approximated by piecewise-affine functions, the optimal control has a closed-form state-feedback realization. The optimal feedback control law, however, has a centralized structure and requires instantaneous access to the state of the entire network that may lead to prohibitive communication requirements in large-scale complex networks. We subsequently examine the design of a decentralized optimal feedback controller with a one-hop information structure, wherein the optimum outflow rate from each segment of the network depends only on the state of that segment and the state of the segments immediately downstream. The decentralization is based on the relaxation of constraints that depend on state variables that are unavailable according to the information structure. The resulting decentralized control scheme has a simple closed-form representation and is scalable to arbitrary large networks; moreover, we demonstrate that, with respect to certain meaningful performance indexes, the performance loss due to decentralization is zero; namely, the centralized optimal controller has a decentralized realization with a one-hop information structure and is obtained at no computational/communication cost.