Output controllability and observability of mix-valued logic control networks

Yuyang Zhao; Yang Liu; Yuyang Zhao; Yang Liu

doi:10.3934/mmc.2021013

Mathematical Modelling and Control

2021, Volume 1, Issue 3: 145-156. doi: 10.3934/mmc.2021013

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Research article

Output controllability and observability of mix-valued logic control networks

Yuyang Zhao ,
Yang Liu ^,

College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China

Received: 26 May 2021 Accepted: 13 July 2021 Published: 31 August 2021

This paper focuses on output controllability and observability of mix-valued logic control networks (MLCNs), of which the updating of outputs is determined by both inputs and states via logical rules. First, as for output controllability, the number of different control sequences are derived to steer a MLCN from a given initial state to a destination output in a given number of time steps via semi-tensor product method. By construsting the output controllability matrix, criteria for the output controllability are obtained. Second, to solve the problem of observability, we construct an augmented MLCN with the same transition matrix, and use the set controllability approach to determine the observability of MLCNs. Finally, a hydrogeological example is presented to verify the obtained results.
- M-valued logic control networks,
- output controllability,
- observability,
- semi-tensor product
Citation: Yuyang Zhao, Yang Liu. Output controllability and observability of mix-valued logic control networks[J]. Mathematical Modelling and Control, 2021, 1(3): 145-156. doi: 10.3934/mmc.2021013

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Abstract

This paper focuses on output controllability and observability of mix-valued logic control networks (MLCNs), of which the updating of outputs is determined by both inputs and states via logical rules. First, as for output controllability, the number of different control sequences are derived to steer a MLCN from a given initial state to a destination output in a given number of time steps via semi-tensor product method. By construsting the output controllability matrix, criteria for the output controllability are obtained. Second, to solve the problem of observability, we construct an augmented MLCN with the same transition matrix, and use the set controllability approach to determine the observability of MLCNs. Finally, a hydrogeological example is presented to verify the obtained results.

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