After discussing boundary control for delay systems in Chap. 2, we now focus on sampled-data control, crucial for real-world systems. Chapter 3 explores distributed sampled-data control of nonlinear PDEs, particularly the KSE. We design locally stabilizing controllers for 1D and 2D systems using spatially distributed measurements. We employ the spatial decomposition (or sampling in space) method introduced in [1, 2] for the heat equation. We also introduce a switched sampled-data approach to reduce energy consumption and stabilize the system by using mobile actuators. We apply both continuous-time and sampled-data feedback to stabilize a PDE-PDE cascade system, demonstrating the versatility of our control strategies. Finally we present distributed stabilization of KdVB equation in the presence of constant delay.

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Sampled-Data and Delayed Control of PDE Systems

  • Wen Kang,
  • Emilia Fridman

摘要

After discussing boundary control for delay systems in Chap. 2, we now focus on sampled-data control, crucial for real-world systems. Chapter 3 explores distributed sampled-data control of nonlinear PDEs, particularly the KSE. We design locally stabilizing controllers for 1D and 2D systems using spatially distributed measurements. We employ the spatial decomposition (or sampling in space) method introduced in [1, 2] for the heat equation. We also introduce a switched sampled-data approach to reduce energy consumption and stabilize the system by using mobile actuators. We apply both continuous-time and sampled-data feedback to stabilize a PDE-PDE cascade system, demonstrating the versatility of our control strategies. Finally we present distributed stabilization of KdVB equation in the presence of constant delay.