On robust set stability and set stabilization of probabilistic Boolean control networks

Highlights：

• The largest robust invariant set and the largest robust control invariant set with probability one are calculated for the first time.

• The criterion to determine the finite-time robust set stability and robust set stabilization with probability one are firstly derived. The results obtained can be used to study several unsolved disturbed PBCN problems, including finite-time robust output tracking, robust synchronization and robust partial stabilization with probability one.

• A design procedure is proposed to calculate all the time-optimal robust feedback stabilizers via antecedence solution technique. Compared with the traditional design method, the controls can be obtained directly from the nonzero columns of the truth matrices, in which the computation involved can be easily executed by MATLAB.

摘要

•The largest robust invariant set and the largest robust control invariant set with probability one are calculated for the first time.•The criterion to determine the finite-time robust set stability and robust set stabilization with probability one are firstly derived. The results obtained can be used to study several unsolved disturbed PBCN problems, including finite-time robust output tracking, robust synchronization and robust partial stabilization with probability one.•A design procedure is proposed to calculate all the time-optimal robust feedback stabilizers via antecedence solution technique. Compared with the traditional design method, the controls can be obtained directly from the nonzero columns of the truth matrices, in which the computation involved can be easily executed by MATLAB.

论文关键词：Probabilistic Boolean control networks,The largest robust invariant set,Robust set stability,Robust set stabilization,Semi-tensor product of matrices

论文评审过程：Received 17 August 2021, Revised 22 November 2021, Accepted 27 January 2022, Available online 6 February 2022, Version of Record 6 February 2022.