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H ∞ boundary control for a class of nonlinear stochastic parabolic distributed parameter systems
Author(s) -
Zhang XiuMei,
Wu HuaiNing
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4646
Subject(s) - mathematics , nonlinear system , boundary (topology) , exponential stability , control theory (sociology) , distributed parameter system , semigroup , mathematical analysis , partial differential equation , control (management) , computer science , physics , quantum mechanics , artificial intelligence
Summary This paper addresses the problem of H ∞ boundary control for a class of nonlinear stochastic distributed parameter systems expressed by parabolic stochastic partial differential equations (SPDEs) of Itô type. A simple but effective H ∞ boundary static output feedback (SOF) control scheme with collocated boundary measurement is introduced to ensure the local exponential stability in the mean square sense with an H ∞ performance. By using the semigroup theory, the disturbance‐free closed‐loop well‐posedness analysis is first given. Then, based on the SPDE model, a general linear matrix inequality based H ∞ boundary SOF control design is provided via Lyapunov technique and infinite‐dimensional infinitesimal operator, such that the disturbance‐free closed‐loop system is locally exponentially stable in the mean square sense and the H ∞ performance of disturbance attenuation can also be achieved in the presence of disturbances. Finally, simulation results on a stochastic Fisher‐Kolmogorov‐Petrovsky‐Piscounov equation illustrate the effectiveness of the proposed method.