TY - GEN

T1 - Fast moving horizon estimation for a distributed parameter system

AU - Jang, Hong

AU - Kim, Kwang Ki K.

AU - Lee, Jay H.

AU - Braatz, Richard D.

PY - 2012

Y1 - 2012

N2 - Partial differential equations (PDEs) pose a challenge for control engineers, both in terms of theory and computational requirements. PDEs are usually approximated by ordinary differential or partial difference equations via the finite difference method, resulting in a high-dimensional state-space system. The obtained system matrix is often symmetric, which allows this high-dimensional system to be decoupled into a set of single-dimensional systems using the state coordinate transformation defined by a singular value decomposition. Any linear constraints in the original control problem can also be simplified by replacement by an ellipsoidal constraint. This reformulated moving horizon estimation (MHE) problem can be solved in orders of magnitude lower computation time than the original MHE problem, by employing an analytical solution obtained by moving the ellipsoidal constraint to the objective function as a penalty weighted by a decreasing penalty parameter. The proposed MHE algorithm is demonstrated for a one-dimensional diffusion in which the concentration field is estimated using distributed sensors.

AB - Partial differential equations (PDEs) pose a challenge for control engineers, both in terms of theory and computational requirements. PDEs are usually approximated by ordinary differential or partial difference equations via the finite difference method, resulting in a high-dimensional state-space system. The obtained system matrix is often symmetric, which allows this high-dimensional system to be decoupled into a set of single-dimensional systems using the state coordinate transformation defined by a singular value decomposition. Any linear constraints in the original control problem can also be simplified by replacement by an ellipsoidal constraint. This reformulated moving horizon estimation (MHE) problem can be solved in orders of magnitude lower computation time than the original MHE problem, by employing an analytical solution obtained by moving the ellipsoidal constraint to the objective function as a penalty weighted by a decreasing penalty parameter. The proposed MHE algorithm is demonstrated for a one-dimensional diffusion in which the concentration field is estimated using distributed sensors.

KW - Distributed parameter system

KW - Ellipsoid constraint

KW - Lagrangian method

KW - Moving horizon estimation

KW - Partial differential equation

KW - Singular value decomposition

UR - http://www.scopus.com/inward/record.url?scp=84872578761&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84872578761

SN - 9781467322478

T3 - International Conference on Control, Automation and Systems

SP - 533

EP - 538

BT - ICCAS 2012 - 2012 12th International Conference on Control, Automation and Systems

T2 - 2012 12th International Conference on Control, Automation and Systems, ICCAS 2012

Y2 - 17 October 2012 through 21 October 2012

ER -