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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 control policy, which minimizes a desired objective, where the objective value depends on the future evolution of the system (the state of the system), which, in turn, depends on the control 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 information between subsystems with shared control variables. This article presents a method, based on the asynchronous alternating directions method of multiplier algorithm, which extends these techniques to subsystems with shared control and state variables, while maintaining similar communication structure. The method is used as the basis for splitting network flow control problems into many subnetwork control problems with shared boundary conditions. The decentralized and parallel nature of the method permits high scalability with respect to the size of the network. For highly nonconvex applications, an efficient method, based on adjoint gradient computations, is presented for solving subproblems with shared state. The method is applied to decentralized, coordinated ramp metering and variable speed limit control on a realistic freeway network model using distributed model predictive control.