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A convex formulation for robust control of bilinear positive systems with evolutionary dynamics

Babazadeh, M ; Sharif University of Technology | 2023

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  1. Type of Document: Article
  2. DOI: 10.1109/TCST.2022.3222619
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2023
  4. Abstract:
  5. 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 H2 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 H2 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). © 1993-2012 IEEE
  6. Keywords:
  7. Convex optimization ; Evolutionary process ; Min-max problems ; Polytopic uncertainty ; Positive systems
  8. Source: IEEE Transactions on Control Systems Technology ; Volume 31, Issue 3 , 2023 , Pages 1345-1354 ; 10636536 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/9965962