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Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks

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Abstract

This paper addresses two kinds of optimal control problems of probabilistic mix-valued logical control networks by using the semi-tensor product of matrices, and presents a number of new results on the optimal finite-horizon control and the first-passage model based control problems, respectively. Firstly, the probabilistic mix-valued logical control network is expressed in an algebraic form by the semi-tensor product method, based on which the optimal finite-horizon control problem is studied and a new algorithm for choosing a sequence of control actions is established to minimize a given cost functional over finite steps. Secondly, the first-passage model of probabilistic mix-valued logical networks is given and a new algorithm for designing the optimal control scheme is proposed to maximize the corresponding probability criterion. Finally, an illustrative example is studied to support our new results/algorithms.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    ZhenBin Liu, YuZhen Wang & HaiTao Li

  2. Science and Information College, Qingdao Agricultural University, Qingdao, 266109, China

    ZhenBin Liu

Authors
  1. ZhenBin Liu
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  2. YuZhen Wang
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  3. HaiTao Li
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Correspondence to YuZhen Wang.

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Liu, Z., Wang, Y. & Li, H. Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks. Sci. China Inf. Sci. 57, 1–10 (2014). https://doi.org/10.1007/s11432-013-4796-7

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  • DOI: https://doi.org/10.1007/s11432-013-4796-7

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