Seminar Details
2013-03-19 (14.00) : On solving KKT linear systems arising in Model Predictive Control
At Euler building
Organized by Mathematical Engineering
Speaker :
Nicola Mastronardi (Istituto per le Applicazioni del Calcolo M. Picone, Consiglio Nazionale delle Ricerche, sede di Bari )
Abstract :
The approximate solution of Model Predictive Control problems [2,3,4] is often computed in an iterative fashion, requiring to compute, at each iteration, the solution of a quadratic optimization problem. The most expensive part of the latter problem is the solution of symmetric indefinite KKT systems, where the involved matrices are highly structured.
Recently, an algorithm for computing a block anti--triangular factorization of symmetric indefinite matrices, based on orthogonal transformations, has been proposed[1].
The aim of this talk is to show that such a factorization, implemented in a suitable way, can be efficiently used for solving the mentioned KKT linear systems. This talk is based on a joint work with Paul Van Dooren.
References : [1] N. Mastronardi, P. Van Dooren, The anti-triangular factorization of symmetric matrices, SIAM Journal on Matrix Analysis and Applications, to appear.--
[2] C. Kirches, H. Bock, J.P. Schloder, S. Sager, A factorization with update procedures for a KKT matrix arising in direct optimal control, Mathematical Programming Computation, 3(4), pp.319348, 2011 --
[3] Y. Wang, S. Boyd, Fast Model Predictive Control Using Online Optimization, IEEE Transactions on Control Systems Technology, 18(2), pp.267-278, 2010 -- [4] V.M. Zavala, C.D. Laird, L,T. Biegler,
A fast moving horizon estimation algorithm based on nonlinear programming sensitivity, Journal of Process Control, 18(9), pp.876-884, 2008.