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Finite-time output tracking of probabilistic Boolean control networks.

Authors :
Zhang, Anguo
Li, Lulu
Li, Yuanyuan
Lu, Jianquan
Source :
Applied Mathematics & Computation. Dec2021, Vol. 411, pN.PAG-N.PAG. 1p.
Publication Year :
2021

Abstract

• The problem of system tracking a single ROS is considered in the first part. The necessary and sufficient condition for the output tracking problem of PBCNs to be solvable is obtained. Based on this condition, the event-based controller has been designed to solve the considered tracking problem. Compared with [18,34], the number of control switchings for the designed controller can be reduced effectively. • A necessary and sufficient condition that the TVROT is trackable in probability one starting from the given initial state is obtained. Moreover, a new strategy is offered to design the control sequence. Compared with [31], we extend the necessary and sufficient condition that for the given initial state, the system can realize output tracking of TVROT from BNs to PBNs. • An effective algorithm is provided to solve the maximum tracking probability for the given initial state which can not track TVROT with probability one. Compared with [26], the problem of the system tracking a TVROT rather than a fixed ROS is considered in this paper, and time-variant controller has been designed to make the state of the system track TVROT from the given initial state with maximum probability. This paper mainly concentrates on the issue of finite-time output tracking of probabilistic Boolean control networks (PBCNs). Two kinds of problems are considered: (1) the system tracks a fixed reference output signal (ROS); (2) the system tracks a time variant reference output trajectory (TVROT). For the first problem, we design an effective event-triggered controller to realize output tracking in probability one. An algorithm is offered to find the control invariant subset (CIS) of a set, and a triggering set sequence is constructed based on the CIS. Next, a necessary and sufficient condition is proposed to judge whether the system is trackable in probability one. For the second problem, a criterion is given to judge whether the initial state can generate TVROT with probability one and an algorithm is then provided to solve the corresponding control sequence. Furthermore, a profit function is established to solve the maximum tracking probability for the initial state which can not generate TVROT with probability one. Lastly, two examples are offered to explain the theoretical results. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00963003
Volume :
411
Database :
Academic Search Index
Journal :
Applied Mathematics & Computation
Publication Type :
Academic Journal
Accession number :
152272416
Full Text :
https://doi.org/10.1016/j.amc.2021.126413