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Robust feedback switching control: dynamic programming and viscosity solutions

Abstract : We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non standard class of switching controls introduced in this paper. The adverse player (nature) chooses open-loop controls that represent the so-called Knightian uncertainty, i.e., misspecifications of the model. The (half) game switcher versus nature is then formulated as a two-step (robust) optimization problem. We develop the stochastic Perron method in this framework, and prove that it produces a viscosity sub and supersolution to a system of Hamilton-Jacobi-Bellman (HJB) variational inequalities, which envelope the value function. Together with a comparison principle, this characterizes the value function of the game as the unique viscosity solution to the HJB equation, and shows as a byproduct the dynamic programming principle for robust feedback switching control problem.
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Contributor : Huyên Pham <>
Submitted on : Thursday, June 30, 2016 - 5:25:59 PM
Last modification on : Friday, March 27, 2020 - 3:32:01 AM
Document(s) archivé(s) le : Saturday, October 1, 2016 - 1:11:24 PM


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to appear in SIAM Journal on Control and Optimization.


  • HAL Id : hal-01066954, version 2
  • ARXIV : 1409.6233


Erhan Bayraktar, Andrea Cosso, Huyen Pham. Robust feedback switching control: dynamic programming and viscosity solutions. 2016. ⟨hal-01066954v2⟩



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