Finite horizon tracking control of probabilistic Boolean control networks |
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| Institution: | 1. School of Mathematics, Shandong University, Jinan 250100, China;2. School of Electrical and Electronic Engineering, Shandong University of Technology, Zibo 255000, China;1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, PR China;2. Institute of Automation, Qufu Normal University, Qufu 273165, PR China;1. School of Mathematics, Southeast University, Nanjing 210096, China;2. School of Information Engineering, Huzhou University, Huzhou 313000, China;3. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China;1. School of Mathematics, Shandong University, Jinan 250100, People’s Republic of China;2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Republic of Singapore;1. School of Mathematical Science, Shandong Normal University, Jinan 250014, PR China;2. School of Control Science and Engineering, Shandong University, Jinan 250061, PR China |
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| Abstract: | In this paper, the finite horizon tracking control problem of probabilistic Boolean control networks (PBCNs) is studied. For a given reference output trajectory, two trackability definitions are introduced according to whether the tracking probability is 1. Under the framework of the semi-tensor product, some necessary and sufficient conditions are obtained to determine whether the reference output trajectory is trackable with probability (probability one) by a PBCN starting from a given initial state. Based on this, two algorithms are proposed to determine the maximum tracking probability and the corresponding optimal control policy sequence. By determining the tracking error of the reference output trajectory, two related optimal control problems are considered: one is to minimize the expected value of the total tracking error, and the other is to minimize the maximum tracking error. Inspired by dynamic programming, corresponding algorithms are given to solve these two problems. Finally, two examples are given to verify the validity and correctness of the results. |
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