Reconstructing the State of a Boolean Control Network Via State Feedback

The goal of this paper is to investigate under what conditions a Boolean Control Network admits a state feedback control law that makes the resulting Boolean Network reconstructable. Starting from an algebraic representation of the Boolean Control Network, we first propose a result that allows to si...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2023-09, Vol.68 (9), p.1-8
Main Authors: Fornasini, Ettore, Valcher, Maria Elena
Format: Article
Language:English
Subjects:
Algebra
Biomedical measurement
Boolean algebra
Control systems
Control theory
Fault detection
Feedback control
Numerical models
Polynomials
State feedback
State-space methods
Time measurement
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Summary:The goal of this paper is to investigate under what conditions a Boolean Control Network admits a state feedback control law that makes the resulting Boolean Network reconstructable. Starting from an algebraic representation of the Boolean Control Network, we first propose a result that allows to significantly reduce the problem size, and hence to mitigate the curse of dimensionality that typically arises when dealing with logical systems of very large size. Subsequently, we provide a necessary and sufficient condition for the problem solvability that relies on the algebra of noncommutative polynomials. Finally, when such a condition holds, we present a procedure to design a possible state feedback controller that achieves the desired result.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3218617