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Generalized Dual Dynamic Programming for Infinite Horizon Problems in Continuous State and Action Spaces

Joseph Warrington(warrington***at***control.ee.ethz.ch)
Paul Beuchat(beuchatp***at***control.ee.ethz.ch)
John Lygeros(lygeros***at***control.ee.ethz.ch)

Abstract: 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 action (or 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.

Keywords: Dynamic programming, infinite horizon, discrete time, optimal control

Category 1: Other Topics (Dynamic Programming )

Category 2: Applications -- Science and Engineering (Control Applications )

Citation: Automatic Control Lab, ETH Zurich, Switzerland, November 2017

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Entry Submitted: 11/01/2017
Entry Accepted: 11/01/2017
Entry Last Modified: 11/01/2017

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