Using modified Centroidal Voronoi Tessellations in kernel partitioning for optimal actuator and sensor selection of parabolic PDEs with static output feedback
Michael A. Demetriou · 2017
This work presents a methodology that utilizes computational geometry methods to design controllers and actuators in spatially distributed systems governed by partial differential equations. Utilizing earlier works on the modification of Centroidal Voronoi Tessellations (CVT), a methodology is presented that simultaneously designs the actuator and sensor locations, and the static output feedback. This approach which significantly reduces the control design complexity firsts assumes a virtual idealized actuator to design the optimal feedback gain. Then the modified CVT is applied to both the virtual actuator and the feedback kernel to obtain both the actuator and sensor locations, respectively. Subsequently, a static feedback gain matrix is designed in order to implement a static output feedback that approximates the idealized input and optimal gain with full state information. Extensive and detailed numerical studies are included to clarify the many aspects of the proposed methodology.