Open AccessH ∞ control design for non‐linear distributed parameter systems with mobile actuators and sensors
Author(s) -
Zhang XiaoWei,
Wu HuaiNing
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.0092
Subject(s) - control theory (sociology) , distributed parameter system , actuator , linear system , projection (relational algebra) , bilinear interpolation , overshoot (microwave communication) , partial differential equation , mathematics , computer science , control (management) , algorithm , artificial intelligence , mathematical analysis , telecommunications , statistics
This study deals with the H ∞ control design problem for a class of non‐linear distributed parameter systems described by parabolic partial differential equations (PDEs) via mobile collocated actuators and sensors. Initially, the spatial domain is decomposed into multiple subdomains according to the number of actuator/sensor pairs and the projection modification algorithm is employed to guarantee each actuator/sensor pair is only capable of moving within the respective subdomain. Subsequently, the well‐posedness of the closed‐loop PDE system is analysed by means of the operator semigroup theory. Then, a control‐plus‐guidance design method for the non‐linear PDE system is developed in the form of bilinear matrix inequalities, such that the resulting closed‐loop system is exponentially stable while satisfying a prescribed H ∞ performance of disturbance attenuation, and the mobile actuator/sensor guidance can enhance the transient performance of the closed‐loop system. Finally, a numerical example and a practical application example are respectively given to show the effectiveness of the proposed design method.