Robust <i>H<sub>∞</sub> </i> Control for Semilinear Parabolic Distributed Parameter Systems With External Disturbances via Mobile Actuators and Sensors
Yaqiang Liu, Jun‐Wei Wang, Zongze Wu, Zhigang Ren, Shengli Xie
Abstract
This article presents a robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H_{\infty }}$ </tex-math></inline-formula> feedback compensator design approach for semilinear parabolic distributed parameter systems (DPSs) with external disturbances via mobile actuators and sensors. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H_{\infty }}$ </tex-math></inline-formula> performance constraint is introduced to deal with the external disturbances from the model and measurement noise. Two types of feedback compensators are designed in terms of the collocated and noncollocated mobile actuators and sensors. By the Lyapunov direct technique, some sufficient conditions based on LMI constraints are proposed for the exponential stability under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H_{\infty }}$ </tex-math></inline-formula> performance constraints in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}^{2}$ </tex-math></inline-formula> -norm. Moreover, the open-loop and closed-loop well-posedness of the semilinear DPSs with external disturbances are analyzed via the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${C_{0}}$ </tex-math></inline-formula> -semigroup theory approach. Finally, extensive numerical simulation results for semilinear DPSs with external disturbances via collocated and noncollocated mobile actuators and sensors are shown to verify the effectiveness of the proposed method.