This note proposes an efficient computational procedure for the continuous time, input constrained, infinite horizon, linear quadratic regulator problem (CLQR). To ensure satisfaction of the constraints, the input is approximated as a piecewise linear function on a finite time discretization. The solution of this approximate problem is a standard quadratic program. A novel lower bound on the infinite dimensional CLQR problem is developed, and the discretization is adaptively refined until a user supplied error tolerance on the CLQR cost is achieved. The offline storage of the required quadrature matrices at several levels of discretization tailors the method for online use as required in model predictive control (MPC). The performance of the proposed algorithm is then compared with the standard discrete time MPC algorithms. The proposed method is shown to be significantly more efficient than standard discrete time MPC that uses a sample time short enough to generate a cost close to the CLQR solution.

Whither discrete time model predictive control?

PANNOCCHIA, GABRIELE;
2015

Abstract

This note proposes an efficient computational procedure for the continuous time, input constrained, infinite horizon, linear quadratic regulator problem (CLQR). To ensure satisfaction of the constraints, the input is approximated as a piecewise linear function on a finite time discretization. The solution of this approximate problem is a standard quadratic program. A novel lower bound on the infinite dimensional CLQR problem is developed, and the discretization is adaptively refined until a user supplied error tolerance on the CLQR cost is achieved. The offline storage of the required quadrature matrices at several levels of discretization tailors the method for online use as required in model predictive control (MPC). The performance of the proposed algorithm is then compared with the standard discrete time MPC algorithms. The proposed method is shown to be significantly more efficient than standard discrete time MPC that uses a sample time short enough to generate a cost close to the CLQR solution.
Pannocchia, Gabriele; Rawlings, J. B.; Mayne, D. Q.; Mancuso, G. M.
File in questo prodotto:
File Dimensione Formato  
06816006.pdf

solo utenti autorizzati

Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 460.67 kB
Formato Adobe PDF
460.67 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pannocchia_IEEE.PDF

accesso aperto

Tipologia: Documento in Post-print
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 371.1 kB
Formato Adobe PDF
371.1 kB Adobe PDF Visualizza/Apri

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: http://hdl.handle.net/11568/516670
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 12
social impact