On the Stability of Receding Horizon Control of Bilinear Parabolic PDE Systems

Y. Ou and E. Schuster

49th IEEE Conference on Decision and Control

Atlanta, Georgia, December 15-17, 2010

Abstract

We propose a framework to solve an optimal control problem for a bilinear parabolic partial differential equation (PDE). We formulate the problem as an abstract bilinear-quadratic regulator (BQR) problem. A receding hori- zon control (RHC) algorithm to solve the problem based on the infinite-dimensional system is proposed and stability of the algorithm for the solution of the BQR problem is studied. A successive approximation approach is used to numerically solve the quadratic optimal control problem subject to the bilinear PDE model associated with the RHC scheme. Finally, the pro- posed approach is applied to the current profile control problem in tokamak plasmas and its effectiveness is demonstrated in simulations.