This article proposes a novel coordinate-descent augmented-Lagrangian (CDAL) solver for linear, possibly parameter-varying, model predictive control (MPC) problems. At each iteration, an augmented Lagrangian (AL) subproblem is solved by coordinate descent (CD), exploiting the structure of the MPC problem. The CDAL solver enjoys three main properties: 1) it is construction-free, in that it avoids explicitly constructing the quadratic programming problem associated with MPC; 2) is matrix-free, as it avoids multiplications and factorizations of matrices; and 3) is library-free, as it can be simply coded without any library dependency, 90-lines of C-code in our implementation. To favor the convergence speed, CDAL employs a reverse cyclic rule for the CD method, the accelerated Nesterov’s scheme for updating the dual variables, a simple diagonal preconditioner, and an efficient coupling scheme between the CD and AL methods. We show that CDAL competes with other state-of-the-art methods, both in the case of unstable linear time-invariant and linear parameter-varying prediction models. © 2023 IEEE.

A Simple and Fast Coordinate-Descent Augmented-Lagrangian Solver for Model Predictive Control

L. Wu;A. Bemporad
2023-01-01

Abstract

This article proposes a novel coordinate-descent augmented-Lagrangian (CDAL) solver for linear, possibly parameter-varying, model predictive control (MPC) problems. At each iteration, an augmented Lagrangian (AL) subproblem is solved by coordinate descent (CD), exploiting the structure of the MPC problem. The CDAL solver enjoys three main properties: 1) it is construction-free, in that it avoids explicitly constructing the quadratic programming problem associated with MPC; 2) is matrix-free, as it avoids multiplications and factorizations of matrices; and 3) is library-free, as it can be simply coded without any library dependency, 90-lines of C-code in our implementation. To favor the convergence speed, CDAL employs a reverse cyclic rule for the CD method, the accelerated Nesterov’s scheme for updating the dual variables, a simple diagonal preconditioner, and an efficient coupling scheme between the CD and AL methods. We show that CDAL competes with other state-of-the-art methods, both in the case of unstable linear time-invariant and linear parameter-varying prediction models. © 2023 IEEE.
2023
Augmented Lagrangian (AL) method
coordinate descent (CD) method
model predictive control (MPC)
File in questo prodotto:
File Dimensione Formato  
A_Simple_and_Fast_Coordinate-Descent_Augmented-Lagrangian_Solver_for_Model_Predictive_Control.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 684.51 kB
Formato Adobe PDF
684.51 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/20.500.11771/27878
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
social impact