This paper investigates the Morgan＇s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is co...This paper investigates the Morgan＇s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an output- decomposed form by constructing a set of consistent outputfriendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan＇s problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan＇s problem is obtained.展开更多
This paper gives an equivalent condition for the observability of Boolean control networks（BCNs） with time-variant delays in states under a mild assumption by using the graph-theoretic method under the framework of ...This paper gives an equivalent condition for the observability of Boolean control networks（BCNs） with time-variant delays in states under a mild assumption by using the graph-theoretic method under the framework of the semi-tensor product of matrices. First, the BCN under consideration is split into a finite number of subsystems with no time delays. Second, the observability of the BCN is verified by testing the observability of the so-called observability constructed path（a special subsystem without time delays） based on graph theory. These results extend the recent related results on the observability of BCNs. Examples are shown to illustrate the effectiveness of the results.展开更多
文摘This paper investigates the Morgan＇s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an output- decomposed form by constructing a set of consistent outputfriendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan＇s problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan＇s problem is obtained.
基金supported by the National Natural Science Foundation of China under Grant Nos.61603109and 51209051the Natural Science Foundation of Heilongjiang Province of China under Grant No.LC2016023+1 种基金the Fundamental Research Funds for the Central Universities under Grant Nos.HEUCFM170406 and HEUCFM170112the State Key Laboratory of Ocean Engineering(Shanghai Jiao Tong University)under Grant No.1415
文摘This paper gives an equivalent condition for the observability of Boolean control networks（BCNs） with time-variant delays in states under a mild assumption by using the graph-theoretic method under the framework of the semi-tensor product of matrices. First, the BCN under consideration is split into a finite number of subsystems with no time delays. Second, the observability of the BCN is verified by testing the observability of the so-called observability constructed path（a special subsystem without time delays） based on graph theory. These results extend the recent related results on the observability of BCNs. Examples are shown to illustrate the effectiveness of the results.
