Eugenio Schuster

Receding Horizon Control of the Magnetic Flux Bilinear PDE based on Sequential Linear Quadratic Control

C. Xu, Y. Ou, E. Schuster

International Congress on Industrial and Applied Mathematics

Vancouver, Canada, July 18-22, 2011

Abstract

We present a framework to solve a finite-time optimal control problem for parabolic partial differential equations (PDE) with diffusivity-interior actuators, which is motivated by the control of the current density profile in tokamak plasmas. The problem is formulated as an abstract bilinear-quadratic regulator (BQR) problem. A receding horizon control scheme is combined with a successive approximation algorithm to numerically solve the quadratic optimal control problem subject to the bilinear PDE. Convergence and stability properties of the combined approach are provided.

Research Funding

Prof. Schuster's research work has been supported by the National Science Foundation (NSF) through the CAREER Award Program and the Basic Plasma Science Program, the U.S. Department of Energy (DOE), the Commonwealth of Pennsylvania, Department of Community and Economic Development, through the Pennsylvania Infrastructure Technology Alliance (PITA), the New York State Energy Research and Development Authority (NYSERDA), national laboratories and private companies.