INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2008; 18:816–830 Published online 9 July 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/rnc.1251 An online active set strategy to overcome the limitations of explicit MPC H. J. Ferreau 1, * ,y , H. G. Bock 2 and M. Diehl 1 1 Optimization in Engineering Center (OPTEC) and Department of Electrical Engineering, K.U. Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium 2 Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany SUMMARY Nearly all algorithms for linear model predictive control (MPC) either rely on the solution of convex quadratic programs (QPs) in real time, or on an explicit precalculation of this solution for all possible problem instances. In this paper, we present an online active set strategy for the fast solution of parametric QPs arising in MPC. This strategy exploits solution information of the previous QP under the assumption that the active set does not change much from one QP to the next. Furthermore, we present a modification where the CPU time is limited in order to make it suitable for strict real-time applications. Its performance is demonstrated with a challenging test example comprising 240 variables and 1191 inequalities, which depends on 57 parameters and is prohibitive for explicit MPC approaches. In this example, our strategy allows CPU times of well below 100 ms per QP and was about one order of magnitude faster than a standard active set QP solver. Copyright # 2007 John Wiley & Sons, Ltd. Received 18 October 2006; Revised 30 April 2007; Accepted 29 May 2007 KEY WORDS: model predictive control; parametric quadratic programming; online active set strategy 1. INTRODUCTION The fast and reliable solution of convex quadratic programming (QP) problems in real time is a crucial ingredient of most algorithms for both linear and nonlinear model predictive control (MPC). The success of linear MPC}where just one QP needs to be solved in each sampling time}can even be attributed to the fact that highly efficient and reliable methods for QP solution *Correspondence to: H. J. Ferreau, Optimization in Engineering Center (OPTEC) and Department of Electrical Engineering, K.U. Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium. y E-mail: joachim.ferreau@esat.kuleuven.be Contract/grant sponsor: REGINS-PREDIMOT European project Contract/grant sponsor: Research Council KUL; contract/grant number: CoE EF/05/006 Contract/grant sponsor: Belgian Federal Science Policy Office; contract/grant number: IUAP P6/04 Copyright # 2007 John Wiley & Sons, Ltd.