A Fast Condensing Method for Solution of Linear-Quadratic Control Problems

Gianluca Frison, John Bagterp Jørgensen

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Abstract

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper we consider a condensing (or state elimination) method to solve an extended version of the LQ control problem, and we show how to exploit the structure of this problem to both factorize the dense Hessian matrix and solve the system. Furthermore, we present two efficient implementations. The first implementation is formally identical to the Riccati recursion based solver and has a computational complexity that is linear in the control horizon length and cubic in the number of states. The second implementation has a computational complexity that is quadratic in the control horizon length as well as the number of states. When the state dimension is high, this implementation is faster than the Riccati recursion based implementation.
Original languageEnglish
Title of host publication52nd IEEE Conference on Decision and Control
PublisherIEEE
Publication date2013
Pages7715-7720
ISBN (Print)978-1-4673-5716-6
DOIs
Publication statusPublished - 2013
Event52nd IEEE Conference on Decision and Control (CDC 2013) - Congress Centre Firenze, Florence, Italy
Duration: 10 Dec 201313 Dec 2013
http://cdc2013.units.it/

Conference

Conference52nd IEEE Conference on Decision and Control (CDC 2013)
LocationCongress Centre Firenze
CountryItaly
CityFlorence
Period10/12/201313/12/2013
Internet address

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