Predictive control of parabolic PDEs with boundary control actuation

• Published in: Chemical engineering science Vol. 61; no. 18; pp. 6239 - 6248
• Main Authors: Dubljevic, Stevan, Christofides, Panagiotis D.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.09.2006; Elsevier
• Subjects: Applied sciences; Boundary control; Chemical engineering; Diffusion–reaction processes; Dissipative systems; Exact sciences and technology; Input/state constraints; Model predictive control; Parabolic PDEs; Model predictive control; Diffusion–reaction processes; Boundary control; Dissipative systems; Input/state constraints; Parabolic PDEs; Closed loop; Stability; Forecast model; Steady state; Partial differential equation; Control constraint; Diffusion; Diffusion-reaction processes; Predictive control; State constraint
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/j.ces.2006.05.041

This work focuses on predictive control of linear parabolic partial differential equations (PDEs) with boundary control actuation subject to input and state constraints. Under the assumption that measurements of the PDE state are available, various finite-dimensional and infinite-dimensional predictive control formulations are presented and their ability to enforce stability and constraint satisfaction in the infinite-dimensional closed-loop system is analyzed. A numerical example of a linear parabolic PDE with unstable steady state and flux boundary control subject to state and control constraints is used to demonstrate the implementation and effectiveness of the predictive controllers.