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Observer‐based <i>H</i><sub><i>∞</i></sub> control of a stochastic Korteweg–de Vries–Burgers equation

Wen Kang, Xiao‐Nan Wang, Kai‐Ning Wu, Qing Li, Zhijie Liu

2021International Journal of Robust and Nonlinear Control16 citationsDOI

Abstract

Abstract This article mainly deals with observer‐based H ∞ control problem for a stochastic Korteweg–de Vries–Burgers equation under point or averaged measurements. Due to the nonlinearity of the stochastic partial differential equations, special emphases are given to computation complexity. By constructing an appropriate Lyapunov functional, we derive sufficient conditions in terms of linear matrix inequalities to guarantee the internal exponential stability and H ∞ performance of the perturbed closed‐loop system by means of the Lyapunov approach. Consistent simulation results that support the proposed theoretical statements are provided. Finally, we have made important instructions for future research directions.

Topics & Concepts

Burgers' equationMathematicsObserver (physics)Nonlinear systemExponential stabilityLyapunov functionApplied mathematicsStability (learning theory)Exponential functionComputationControl theory (sociology)Differential equationMathematical analysisControl (management)Computer sciencePhysicsAlgorithmQuantum mechanicsMachine learningArtificial intelligenceStability and Controllability of Differential EquationsAdvanced Mathematical Physics ProblemsQuantum chaos and dynamical systems
Observer‐based <i>H</i><sub><i>∞</i></sub> control of a stochastic Korteweg–de Vries–Burgers equation | Litcius