A Convex Formulation for Robust Control of Bilinear Positive Systems With Evolutionary Dynamics

In this article, optimal control of bilinear positive systems with uncertain evolutionary dynamics is studied. The first objective is to determine optimal control signals such that the effect of the disturbance signals on the outputs of the nominal dynamics is minimized in terms of the <inline-fo...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on control systems technology Vol. 31; no. 3; pp. 1 - 10
Main Authors: Babazadeh, Maryam, Akbari, Sanaz
Format: Journal Article
Language:English
Published: New York IEEE 01.05.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Antibodies
Apexes
Computational geometry
Control systems
Convex functions
Convex optimization
Convexity
evolutionary process
HIV
Human immunodeficiency virus
Iterative methods
Linear systems
min-max problems
Optimal control
Optimization
Performance indices
polytopic uncertainty
positive systems
Robust control
Viruses (medical)
ISSN:1063-6536, 1558-0865
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, optimal control of bilinear positive systems with uncertain evolutionary dynamics is studied. The first objective is to determine optimal control signals such that the effect of the disturbance signals on the outputs of the nominal dynamics is minimized in terms of the <inline-formula> <tex-math notation="LaTeX">\mathcal{H}_2</tex-math> </inline-formula> norm performance index. Properties of the positive systems, Metzler matrices, and the exploitable structure of the problem are utilized to show that the underlying problem is representable as a standard convex optimization problem. Next, the optimal strategy is examined in the presence of polytopic uncertainties. In this case, the optimization problem is a semi-infinite min-max problem. It is shown that under some assumptions, the underlying problem is equivalent to a finite min-max problem, i.e., it suffices to check only the vertices of the polytopic set for <inline-formula> <tex-math notation="LaTeX">\mathcal{H}_2</tex-math> </inline-formula> norm minimization. The proposed approach for polytopic bilinear positive systems is non-iterative, does not involve parameter tuning or nonsmooth optimization algorithms, and can be solved using off-the-shelf solvers. The effectiveness of the proposed approach is investigated for the optimal combination therapy of human immunodeficiency virus (HIV).
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1063-6536
1558-0865
DOI:10.1109/TCST.2022.3222619