Distributed Optimization for Shared State Systems: Applications to Decentralized Freeway Control via Subnetwork Splitting


Optimal control problems on dynamical systems are concerned with finding a management policy, that minimizes a desired objective, where the objective worth depends on the longer term evolution of the system (the state of the system), which, in flip, depends on the management policy. For systems which contain subsystems that are disjoint across the state variables, distributed optimization techniques exist, which iteratively update subsystems concurrently and then exchange info between subsystems with shared management variables. This article presents a method, based on the asynchronous alternating directions method of multiplier algorithm, which extends these techniques to subsystems with shared management and state variables, whereas maintaining similar Communication structure. The method is employed as the basis for splitting network flow management issues into many subnetwork control issues with shared boundary conditions. The decentralized and parallel nature of the tactic permits high scalability with respect to the dimensions of the network. For highly nonconvex applications, an economical method, based on adjoint gradient computations, is presented for solving subproblems with shared state. The tactic is applied to decentralized, coordinated ramp metering and variable speed limit management on a practical freeway network model using distributed model predictive control.

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