A rapid PDE-based optimization methodology for temperature control and other mixed stochastic and deterministic systems

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Abstract

Abstract: The optimal timing of temperature control generally leads to analytically intractable problems: the state variables' changes in time may be continuous and/or in steps, and may be deterministic and/or stochastic. This problem can be specified concisely as a partial differential equation (PDE), and rapidly solved numerically on a PC (typically a million times faster than exhaustive simulation). By solving the PDE, we can estimate many of the system's physical and/or economic behaviours. We also present a rapid and robust numerical procedure for optimizing the control policy; these methods also have wide applicability in engineering, micro-economics and financial economics. © 2011 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)1523-1530
Number of pages7
JournalEnergy and Buildings
Volume43
Issue number7
DOIs
Publication statusPublished - Jul 2011

Keywords

  • Cyclic schedule
  • Deterministic inventory theory
  • Existence of optimal policies
  • Hamilton-Jacobi-Bellman equation
  • Infinite linear programming duality
  • Optimal temperature control
  • Semi-Markov decision process

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