On Computing Solutions to the Continuous Time Constrained Linear Quadratic Regulator

Author

Pannocchia, Gabriele ; Rawlings, James B. ; Mayne, David Q. ; Marquardt, Wolfgang

Author_Institution

Dept. of Chem. Eng., Univ. of Pisa, Pisa, Italy

Volume

55

Issue

9

fYear

2010

Firstpage

2192

Lastpage

2198

Abstract

We propose in this note a method for computing the solution to the infinite horizon continuous-time constrained linear quadratic regulator. The method is based on two main ingredients: a multigrid method for placing a finite number of time intervals, and a piece-wise linear parameterization of the input within the intervals. The input values at the decision-time points and slopes within the time intervals are computed via quadratic programs (QPs). The grids are gradually refined to efficiently improve the accuracy of the solution, and the required matrices and vectors for all QPs are computed offline and stored to improve the online efficiency. Two examples are presented to show the main characteristics of the proposed method.

Keywords

continuous time systems; linear quadratic control; quadratic programming; finite number; infinite horizon continuous-time constrained linear quadratic regulator; multigrid method; piecewise linear parameterization; quadratic programs; time intervals; Actuators; Continuous time systems; Grid computing; Infinite horizon; Piecewise linear techniques; Predictive control; Predictive models; Regulators; Time factors; Vectors; Constrained linear quadratic regulator (CLQR); continuous-time linear systems; model predictive control (MPC); quadratic programs (QPs);

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2053478

Filename

5491092