Controllability and Observability of Boolean Control Networks With Time-Variant Delays in States

• Published in: IEEE transaction on neural networks and learning systems Vol. 24; no. 9; pp. 1478 - 1484
• Main Authors: Zhang, Lijun, Zhang, Kuize
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Biological neural networks; Boolean algebra; Boolean control network; Computer science; control theory; systems; Construction; Control systems; Controllability; Delay; Delay effects; Delays; Dynamical systems; Dynamics; Exact sciences and technology; Forestry; Information retrieval. Graph; Learning systems; Networks; Observability; semi-tensor product of matrices; Studies; Theoretical computing; time delay; Bilinear system; Tensor product; Boolean Network; Matrix product; Control synthesis; time delay; Dynamical system; Computational complexity; Bounded delay; Boolean control network; semi-tensor product of matrices; Time varying system; Algorithm complexity; Discrete time; Controllability; Delay time; Graph method; Time complexity; Observability
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2013.2246187

This brief investigates the controllability and observability of Boolean control networks with (not necessarily bounded) time-variant delays in states. After a brief introduction to converting a Boolean control network to an equivalent discrete-time bilinear dynamical system via the semi-tensor product of matrices, the system is split into a finite number of subsystems (constructed forest) with no time delays by using the idea of splitting time that is proposed in this brief. Then, the controllability and observability of the system are investigated by verifying any so-called controllability constructed path and any so-called observability constructed paths in the above forest, respectively, which generalize some recent relevant results. Matrix test criteria for the controllability and observability are given. The corresponding control design algorithms based on the controllability theorems are given. We also show that the computing complexity of our algorithm is much less than that of the existing algorithms.