An online active set strategy to overcome the limitations of explicit MPC

TLDR

Nearly all linear MPC algorithms either solve convex QPs in real time or precompute explicit solutions for all instances. This paper proposes an online active‑set strategy to rapidly solve parametric QPs in MPC. The method reuses the previous QP’s active set, assuming minimal change, and incorporates a CPU‑time cap to suit hard real‑time constraints. On a 240‑variable, 1191‑inequality benchmark with 57 parameters, the strategy achieves sub‑100 ms per QP, roughly ten times faster than a standard active‑set solver. © 2007 John Wiley & Sons, Ltd.

Abstract

Abstract 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.