Sampled-Data State-Feedback Stabilization of Probabilistic Boolean Control Networks: A Control Lyapunov Function Approach

• Published in: IEEE transactions on cybernetics Vol. 50; no. 9; pp. 3928 - 3937
• Main Authors: Liu, Jiayang, Liu, Yang, Guo, Yuqian, Gui, Weihua
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.09.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Boolean; Boolean algebra; Control Lyapunov function (CLF); Control systems; Controllability; Feedback control; Liapunov functions; Lyapunov methods; Matrix converters; Partial stabilization; probabilistic Boolean control network (PBCN); Probabilistic logic; sampled-data state-feedback control; semitensor product (STP); set stabilization; Stability analysis; Statistical analysis; Switches
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2019.2932914

This article investigates the partial stabilization problem of probabilistic Boolean control networks (PBCNs) under sample-data state-feedback control (SDSFC) with a control Lyapunov function (CLF) approach. First, the probability structure matrix of the considered PBCN is represented by a Boolean matrix, based on which, a new algebraic form of the system is obtained. Second, we convert the partial stabilization problem of PBCNs into the global set stabilization one. Third, we define CLF and its structural matrix under SDSFC. It is found that the existence of a CLF is equivalent to that of SDSFC. Then, a necessary and sufficient condition is obtained for the existence of CLF under SDSFC, based on which, all possible sample-data state-feedback controllers and corresponding structural matrices of CLF are designed by two different methods. Finally, examples are given to illustrate the efficiency of the obtained results.