Polyhedral control Lyapunov functions (PCLFs) are exploited in this paper to propose a linear model predictive control (MPC) formulation that guarantees a “large” domain of attraction (DoA) even for short horizon. In particular, the terminal region of the proposed finite-horizon MPC formulation is chosen as a level set of an appropriate PCLF. For small dimensional systems, this terminal region can be explicitly computed as an arbitrarily close approximation to the entire (infinite-horizon) stabilizable set. Global stability of the origin is guaranteed by using an “inflated” PCLF as terminal cost. The proposed MPC scheme can be formulated as a (small dimensional) quadratic programming problem by introducing one additional scalar variable. Numerical examples show the main benefits and achievements of the proposed formulation in terms of trade-off between volume of the DoA, computational time and closed-loop performance.

Achieving a large domain of attraction with short-horizon linear MPC via polyhedral Lyapunov functions

GRAMMATICO, SERGIO;PANNOCCHIA, GABRIELE
2013-01-01

Abstract

Polyhedral control Lyapunov functions (PCLFs) are exploited in this paper to propose a linear model predictive control (MPC) formulation that guarantees a “large” domain of attraction (DoA) even for short horizon. In particular, the terminal region of the proposed finite-horizon MPC formulation is chosen as a level set of an appropriate PCLF. For small dimensional systems, this terminal region can be explicitly computed as an arbitrarily close approximation to the entire (infinite-horizon) stabilizable set. Global stability of the origin is guaranteed by using an “inflated” PCLF as terminal cost. The proposed MPC scheme can be formulated as a (small dimensional) quadratic programming problem by introducing one additional scalar variable. Numerical examples show the main benefits and achievements of the proposed formulation in terms of trade-off between volume of the DoA, computational time and closed-loop performance.
2013
9783952417348
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/226039
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 13
social impact