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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to appear in SIAM Journal on Control and Optimization.

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

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

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