Lyapunov-based stabilization control design of space 2-D linear parabolic distributed parameter systems employing mobile sensors and actuators

Xiao-Wei Zhang; Xiang-Jie Pu; Xiaoli Li; Zi-Peng Wang; Xiao-Wei Zhang; Xiang-Jie Pu; Xiaoli Li; Zi-Peng Wang

doi:10.3934/math.2026602

AIMS Mathematics

2026, Volume 11, Issue 5: 14668-14692. doi: 10.3934/math.2026602

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Research article

Lyapunov-based stabilization control design of space 2-D linear parabolic distributed parameter systems employing mobile sensors and actuators

School of Information Science and Technology, Beijing University of Technology, Beijing 100124, China

Received: 27 January 2026 Revised: 24 April 2026 Accepted: 11 May 2026 Published: 25 May 2026
MSC : 35K57, 93C20, 93D15

For the actual physical temporal-space process, the spatial two-dimensional (2-D) case makes more sense. With the increase of space dimension, the difficulty of control design increases sharply. This study investigates the asymptotic stabilization issue for 2-D linear parabolic distributed parameter systems (DPSs) defined over spatial domains, where the control architecture incorporates dynamically collocated sensors and actuators. First, in light of the number of mobile sensor/actuator pairs, the 2-D spatial domain is divided into the corresponding quantity of spatial subdomains. At the same time, the mobile sensor/actuator pairs are forced to move in their respective subdomains under the restriction of projection modification algorithm. Afterwards, based on operator semigroup theory, the well-posedness of open-loop and closed-loop spatial 2-D DPSs is both studied. Aiming at the stabilization control of spatial 2-D DPSs under mobile sensor/actuator pairs, we put forward an integrated design scheme of mobile sensor/actuator guidance and static output feedback controller to guarantee the asymptotic stability of the 2-D closed-loop system. Finally, it can be concluded from a simulation example that the proposed integrated design method is effective.
- space 2-D linear distributed parameter systems,
- static output feedback controller,
- sensor/actuator mobile guidance
Citation: Xiao-Wei Zhang, Xiang-Jie Pu, Xiaoli Li, Zi-Peng Wang. Lyapunov-based stabilization control design of space 2-D linear parabolic distributed parameter systems employing mobile sensors and actuators[J]. AIMS Mathematics, 2026, 11(5): 14668-14692. doi: 10.3934/math.2026602

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Abstract

For the actual physical temporal-space process, the spatial two-dimensional (2-D) case makes more sense. With the increase of space dimension, the difficulty of control design increases sharply. This study investigates the asymptotic stabilization issue for 2-D linear parabolic distributed parameter systems (DPSs) defined over spatial domains, where the control architecture incorporates dynamically collocated sensors and actuators. First, in light of the number of mobile sensor/actuator pairs, the 2-D spatial domain is divided into the corresponding quantity of spatial subdomains. At the same time, the mobile sensor/actuator pairs are forced to move in their respective subdomains under the restriction of projection modification algorithm. Afterwards, based on operator semigroup theory, the well-posedness of open-loop and closed-loop spatial 2-D DPSs is both studied. Aiming at the stabilization control of spatial 2-D DPSs under mobile sensor/actuator pairs, we put forward an integrated design scheme of mobile sensor/actuator guidance and static output feedback controller to guarantee the asymptotic stability of the 2-D closed-loop system. Finally, it can be concluded from a simulation example that the proposed integrated design method is effective.

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