Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 59, Issue 3, Pages 1927-1950Publisher
SIAM PUBLICATIONS
DOI: 10.1137/20M1311028
Keywords
pth moment exponential stabilization; quasi-sure exponential stabilization; G-Brownian motion; G-expectation; discrete-time observations
Categories
Funding
- National Key Research and Development Project of China [2020YFA0714301]
- National Natural Science Foundation of China [61833005, 11871076, 12001100]
- Fundamental Research Funds for the Central Universities [2242020K40238]
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This study offers new insights into the stabilization of stochastic differential equations driven by G-Brownian motion, providing specific discussions on pth moment and quasi-sure exponential stabilization problems through a comparative method. The exponential stabilization for equations with linear coefficients and equations with Lipschitz coefficients are demonstrated using tools from G-Ito stochastic analysis, along with an illustrative example.
We provide feasible criteria for stabilization of stochastic differential equations driven by G-Brownian motion based on discrete-time observations. We extend the results in Ren, Yin, and Sakthivel [Automatica, 95 (2018), pp. 146-151] substantially by adopting a comparative method rather than the Lyapunov function arguments, for the pth moment and quasi-sure exponential stabilization problems. It seems that our pth moment estimates on the gap between the discretized controlled states and the auxiliary system's states are new. Using tools from the G-Ito stochastic analysis, we first show the exponential stabilization for equations with linear coefficients, then for equations with Lipschitz coefficients. An illustrative example is provided.
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