L1 and H-infinity optimal control of positive bilinear systems

Irene Zorzan; Anders Rantzer

doi:10.1109/CDC.2017.8263746

L1 and H-infinity optimal control of positive bilinear systems

Irene Zorzan, Anders Rantzer

University of Padova

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

Abstract

In this paper we consider L1 optimal and H-infinity optimal control problems for a particular class of Positive Bilinear Systems that arise in drug dosage design for HIV treatment. Starting from existent characterizations of the L1-norm for positive systems, a convex formulation for the first problem is provided. As for the H-infinity case, we propose an algorithm based on the iterative solution of a convex feasibility problem, that approximates an H-infinity optimal controller with arbitrary accuracy. A numerical example illustrates the results.

Original language	English
Title of host publication	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Publisher	IEEE - Institute of Electrical and Electronics Engineers Inc.
Pages	727-732
Number of pages	6
Volume	2018-January
ISBN (Electronic)	9781509028733
DOIs	https://doi.org/10.1109/CDC.2017.8263746
Publication status	Published - 2018 Jan 18
Event	56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia Duration: 2017 Dec 12 → 2017 Dec 15 Conference number: 56 http://cdc2017.ieeecss.org/

Conference

Conference	56th IEEE Annual Conference on Decision and Control, CDC 2017
Abbreviated title	CDC 2017
Country/Territory	Australia
City	Melbourne
Period	2017/12/12 → 2017/12/15
Internet address	http://cdc2017.ieeecss.org/

Subject classification (UKÄ)

Control Engineering

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1109/CDC.2017.8263746

Cite this

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title = "L1 and H-infinity optimal control of positive bilinear systems",

abstract = "In this paper we consider L1 optimal and H-infinity optimal control problems for a particular class of Positive Bilinear Systems that arise in drug dosage design for HIV treatment. Starting from existent characterizations of the L1-norm for positive systems, a convex formulation for the first problem is provided. As for the H-infinity case, we propose an algorithm based on the iterative solution of a convex feasibility problem, that approximates an H-infinity optimal controller with arbitrary accuracy. A numerical example illustrates the results.",

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note = "56th IEEE Annual Conference on Decision and Control, CDC 2017, CDC 2017 ; Conference date: 12-12-2017 Through 15-12-2017",

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Zorzan, I & Rantzer, A 2018, L1 and H-infinity optimal control of positive bilinear systems. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. vol. 2018-January, IEEE - Institute of Electrical and Electronics Engineers Inc., pp. 727-732, 56th IEEE Annual Conference on Decision and Control, CDC 2017, Melbourne, Australia, 2017/12/12. https://doi.org/10.1109/CDC.2017.8263746

L1 and H-infinity optimal control of positive bilinear systems. / Zorzan, Irene; Rantzer, Anders.
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Vol. 2018-January IEEE - Institute of Electrical and Electronics Engineers Inc., 2018. p. 727-732.

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

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N2 - In this paper we consider L1 optimal and H-infinity optimal control problems for a particular class of Positive Bilinear Systems that arise in drug dosage design for HIV treatment. Starting from existent characterizations of the L1-norm for positive systems, a convex formulation for the first problem is provided. As for the H-infinity case, we propose an algorithm based on the iterative solution of a convex feasibility problem, that approximates an H-infinity optimal controller with arbitrary accuracy. A numerical example illustrates the results.

AB - In this paper we consider L1 optimal and H-infinity optimal control problems for a particular class of Positive Bilinear Systems that arise in drug dosage design for HIV treatment. Starting from existent characterizations of the L1-norm for positive systems, a convex formulation for the first problem is provided. As for the H-infinity case, we propose an algorithm based on the iterative solution of a convex feasibility problem, that approximates an H-infinity optimal controller with arbitrary accuracy. A numerical example illustrates the results.

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EP - 732

BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017

PB - IEEE - Institute of Electrical and Electronics Engineers Inc.

T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017

Y2 - 12 December 2017 through 15 December 2017

ER -

L1 and H-infinity optimal control of positive bilinear systems

Abstract

Conference

Subject classification (UKÄ)

UN SDGs

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