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

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.