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Structured Linear Quadratic Regulator Design

Schaub, Philipp ; Konigorski, Ulrich (2023)
Structured Linear Quadratic Regulator Design.
27th International Conference on System Theory, Control and Computing. Timisoara, Romania (11.-13.102023)
doi: 10.1109/ICSTCC59206.2023.10308439
Conference or Workshop Item, Bibliographie

Abstract

In this paper, we study linear quadratic regulator (LQR) design subject to linear equality constraints in the controller parameters. Necessary solvability conditions are provided, and a method for choosing the weighting matrices in the quadratic objective function minimized by the constrained LQR is presented. To this end, the problem at hand is transformed into a set of polynomial inequalities that can be solved using Bernstein polynomials. We explicitly show how the requirement of input-output decoupling can be transformed into a set of linear equations in the controller parameters. All control structures that can be transformed into a set of linear equality constraints, e.g. output feedback control, decentralized control, or combinations thereof, can be determined with our method. We demonstrate the proposed method by designing structured optimal controllers for a three-tank system.

Item Type: Conference or Workshop Item
Erschienen: 2023
Creators: Schaub, Philipp ; Konigorski, Ulrich
Type of entry: Bibliographie
Title: Structured Linear Quadratic Regulator Design
Language: English
Date: 10 November 2023
Place of Publication: Timisoara, Romania
Publisher: IEEE
Book Title: 2023 27th International Conference on System Theory, Control and Computing (ICSTCC)
Event Title: 27th International Conference on System Theory, Control and Computing
Event Location: Timisoara, Romania
Event Dates: 11.-13.102023
DOI: 10.1109/ICSTCC59206.2023.10308439
Abstract:

In this paper, we study linear quadratic regulator (LQR) design subject to linear equality constraints in the controller parameters. Necessary solvability conditions are provided, and a method for choosing the weighting matrices in the quadratic objective function minimized by the constrained LQR is presented. To this end, the problem at hand is transformed into a set of polynomial inequalities that can be solved using Bernstein polynomials. We explicitly show how the requirement of input-output decoupling can be transformed into a set of linear equations in the controller parameters. All control structures that can be transformed into a set of linear equality constraints, e.g. output feedback control, decentralized control, or combinations thereof, can be determined with our method. We demonstrate the proposed method by designing structured optimal controllers for a three-tank system.

Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institut für Automatisierungstechnik und Mechatronik
18 Department of Electrical Engineering and Information Technology > Institut für Automatisierungstechnik und Mechatronik > Control Systems and Mechatronics
Date Deposited: 21 Nov 2023 15:22
Last Modified: 31 Jan 2024 15:04
PPN: 515163902
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