Generalized Benders Cuts for Infinite-Horizon Control Problems

We describe a nonlinear generalization of dual dynamic programming theory and its application to value function estimation for deterministic control problems over continuous state and input spaces, in a discrete-time infinite horizon setting. We prove that the result of a one-stage policy evaluation can be used to produce nonlinear lower bounds on the optimal value function that are valid over the entire state space. These bounds reflect the functional form of the system's costs, dynamics, and constraints. We provide an iterative algorithm that produces successively better approximations of the optimal value function, prove some key properties of the algorithm, and describe means of certifying the quality of the output. We demonstrate the efficacy of the approach on systems whose dimensions are too large for conventional dynamic programming approaches to be practical.

Joe Warrington is a Senior Scientist in the Automatic Control Lab at ETH Zurich, Switzerland, and a Simons Fellow at UC Berkeley. His research interests are in optimization, predictive control, and dynamic programming, with applications in energy and transportation networks. His PhD is from ETH Zurich (Dec 2013), carried out under the supervision of Manfred Morari, and he gained the BA and MEng degrees from the University of Cambridge in 2008. He is a holder of the national ABB Research Prize, awarded once every two years for an outstanding PhD thesis completed in the area of control and automation. He returned to ETH in December 2016 after working as an energy consultant at Baringa Partners LLP in London, advising industrial clients and other agencies on strategy, market design, and system modelling.

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