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

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 horizon 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 proposed approach is applied to the current profile control problem in tokamak plasmas and its effectiveness is demonstrated in simulations.