Abstract
In this paper, we investigate the asymptotic stability of the probability density function (pdf) of the states of a class of nonlinear SDEs. We use the Detailed-balance condition as the condition of stability for stochastic processes. Based on the definition of asymptotic stability of the pdf of the SDE, we introduce two notions of probability stability for trajectories of the SDE. The stabilizing feedback controller form is constructed to guarantee the stabilization of the pdf of the SDE as well as stability of the trajectories of the SDE. The proposed method is tested on a real-world process, continuous stirred-tank reactor (CSTR), and the simulation results prove the applicability of the proposed method.
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Namadchian, A., Ramezani, M. Asymptotic stabilization of a class of nonlinear SDEs. Nonlinear Dyn 100, 1431–1440 (2020). https://doi.org/10.1007/s11071-020-05546-1
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DOI: https://doi.org/10.1007/s11071-020-05546-1