TY - JOUR

T1 - Stabilizing tube-based model predictive control: terminal set and cost construction for LPV systems

AU - Hanema, J.

AU - Lazar, M.

AU - Toth, R.

PY - 2017/11

Y1 - 2017/11

N2 - This paper presents a stabilizing tube-based MPC synthesis for LPV systems. We employ terminal constraint sets which are required to be controlled periodically contractive. Periodically (or finite-step) contractive sets are easier to compute and can be of lower complexity than “true” contractive ones, lowering the required computational effort both off-line and on-line. Under certain assumptions on the tube parameterization, recursive feasibility of the scheme is proven. Subsequently, asymptotic stability of the origin is guaranteed through the construction of a suitable terminal cost based on a novel Lyapunov-like metric for compact convex sets containing the origin. A periodic variant on the well-known homothetic tube parameterization that satisfies the necessary assumptions and yields a tractable LPV MPC algorithm is derived. The resulting MPC algorithm requires the on-line solution of a single linear program with linear complexity in the prediction horizon. The properties of the approach are demonstrated by a numerical example.

AB - This paper presents a stabilizing tube-based MPC synthesis for LPV systems. We employ terminal constraint sets which are required to be controlled periodically contractive. Periodically (or finite-step) contractive sets are easier to compute and can be of lower complexity than “true” contractive ones, lowering the required computational effort both off-line and on-line. Under certain assumptions on the tube parameterization, recursive feasibility of the scheme is proven. Subsequently, asymptotic stability of the origin is guaranteed through the construction of a suitable terminal cost based on a novel Lyapunov-like metric for compact convex sets containing the origin. A periodic variant on the well-known homothetic tube parameterization that satisfies the necessary assumptions and yields a tractable LPV MPC algorithm is derived. The resulting MPC algorithm requires the on-line solution of a single linear program with linear complexity in the prediction horizon. The properties of the approach are demonstrated by a numerical example.

KW - Linear parameter-varying systems

KW - Periodic invariance

KW - Tube model predictive control

UR - http://www.scopus.com/inward/record.url?scp=85027588741&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2017.07.046

DO - 10.1016/j.automatica.2017.07.046

M3 - Article

SN - 0005-1098

VL - 85

SP - 137

EP - 144

JO - Automatica

JF - Automatica

ER -