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's method in this framework, and prove that it produces a viscosity subsolution and supersolution to a system of HJB variational inequalities, which envelop 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 by-product the dynamic programming principle for the robust feedback switching control problem.

Robust feedback switching control : dynamic programming and viscosity solutions / E. Bayraktar, A. Cosso, H. Pham. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 54:5(2016), pp. 2594-2628. [10.1137/15M1046903]

Robust feedback switching control : dynamic programming and viscosity solutions

A. Cosso
Secondo
;
2016

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's method in this framework, and prove that it produces a viscosity subsolution and supersolution to a system of HJB variational inequalities, which envelop 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 by-product the dynamic programming principle for the robust feedback switching control problem.
feedback strategies; model uncertainty; optimal switching; stochastic games; stochastic Perron's method; viscosity solutions; control and optimization; applied mathematics
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/931967
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