Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures
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Date
2024-01-19Type
- Conference Paper
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Abstract
This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Value-at-Risk (VaR) of a state function along SDE state distributions. The VaR problem is upper-bounded by an infinite-dimensional Second-Order Cone Program in occupation measures through the use of one-sided Cantelli or Vysochanskii-Petunin inequalities. These upper bounds on the true quantile statistics may be approximated from above by a sequence of Semidefinite Programs in increasing size using the moment-Sum-of-Squares hierarchy when all data is polynomial. Effectiveness of this approach is demonstrated on example stochastic polynomial dynamical systems. Show more
Publication status
publishedExternal links
Book title
2023 62nd IEEE Conference on Decision and Control (CDC)Pages / Article No.
Publisher
IEEEEvent
Organisational unit
02650 - Institut für Automatik / Automatic Control Laboratory
Funding
178890 - Modeling, Identification and Control of Periodic Systems in Energy Applications (SNF)
180545 - NCCR Automation (phase I) (SNF)
Notes
Conference lecture held on December 14, 2023.More
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ETH Bibliography
yes
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