| 摘要: |
| 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 output-friendly 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. |
| 关键词: Boolean control network, Morgan's problem, regular subspace, $y$-friendly subspace, semi-tensor product of matrices |
| DOI： |
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| 基金项目:This work was supported by the National Natural Science Foundation of China (No. 61333001). |
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| Morgan's problem of Boolean control networks |
| S. Fu,Y. Wang,D. Cheng,J. Liu |
| (School of Control Science and Engineering, Shandong University, Jinan Shandong 250061, China;School of Management Science and Engineering, Shandong Normal University, Jinan Shandong 250014, China;Department of Computer Science and Information Systems, Bradley University, Peoria, IL, 61625, U.S.A.) |
| Abstract: |
| 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 output-friendly 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. |
| Key words: Boolean control network, Morgan's problem, regular subspace, $y$-friendly subspace, semi-tensor product of matrices |
