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
VL - 85
SP - 137
EP - 144
JO - Automatica
JF - Automatica
SN - 0005-1098
ER -