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Observability of Boolean Control Networks Using Parallel Extension and Set Reachability.

IEEE Transactions on Neural Networks and Learning Systems

|July 12, 2018

Summary

This study introduces output-feedback observability for Boolean control networks (BCNs), enabling initial state identification from output measurements. New techniques facilitate analysis and establish conditions for observability, linking it to stabilizing logic dynamical systems.

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Area of Science:

Control Theory
Discrete Mathematics
Computer Science

Background:

Boolean control networks (BCNs) are crucial for modeling discrete dynamical systems.
Existing observability definitions for BCNs have limitations.
Identifying system states from limited output data is a fundamental challenge.

Purpose of the Study:

To propose a novel definition of observability for Boolean control networks: output-feedback observability.
To develop new analytical techniques for BCN observability.
To establish connections between observability and system stabilization.

Main Methods:

Reviewing existing observability definitions for BCNs.
Introducing the concept of output-feedback observability.
Developing parallel extension and state transition graph reconstruction techniques.
Analyzing set reachability and deriving new observability criteria.

Main Results:

Output-feedback observability is defined for BCNs where initial states are identifiable from output history.
Parallel extension and state transition graph reconstruction facilitate observability analysis.
New criteria for single-input sequence and arbitrary-input observability are derived.
Output-feedback observability is shown to be equivalent to stabilizing a logic dynamical system with output feedback.
A necessary and sufficient condition for static output feedback observability is presented.

Conclusions:

The proposed output-feedback observability definition offers a comprehensive framework for BCNs.
The developed techniques provide efficient methods for analyzing BCN observability.
The established link to system stabilization offers new control design possibilities.