Estimation of State and Mode for Boolean Networks With Markov Jump Parameters
研究了具有马尔可夫跳变参数的布尔网络的状态与模态估计问题，基于半张量积和贝叶斯定理提出了两种递归矩阵算法，并通过p53-MDM2网络仿真验证了有效性。
First, state estimation for Boolean networks (BNs) with Markov jump parameters (MJPs) is studied in this article. Using semi-tensor product of matrices, the algebraic form of the considered BN with MJPs is constructed. State estimation and mode estimation algorithms based on the output feedback values are presented respectively for the two cases where the output of the observer is deterministic and contains perturbation. Precisely, a recursive matrix-based algorithm, Algorithm 1, is presented to predict the forward state based on minimizing the mean square error. Further, with the help of Bayes Theorem, the optimal system mode estimation is solved and Algorithm 2 is presented to show how to estimate the optimal one from all candidate modes. Finally, a BN with MJPs is constructed from network <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\rm p53-MDM2}$</tex-math> </inline-formula> and the simulation process shows that the results obtained in this article is effective.