Stabilization of Probabilistic Boolean Networks via State-Flipped Control and Reinforcement Learning
Yang Liu, Zejiao Liu, Amol Yerudkar, Carmen Del Vecchio
Abstract
In this article, the state-flipped control technique is explored to investigate the stabilization of probabilistic Boolean networks (PBNs). Changing the values of many nodes from 0 to 1 (or from 1 to 0) is called the state-flipped control. The concepts of fixed point, reachable sets, and finite-time global stabilization of PBNs under state-flipped control are proposed. Several necessary and sufficient conditions for global stabilization are also derived based on the reachable sets of a given state. Furthermore, a model-free reinforcement learning algorithm, namely, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -learning ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> L) is presented to design a flip sequence for any state that steers the state to a given destination state, thereby achieving finite-time global stabilization via state-flipped control. In addition, the process of finding the minimum flip set is proposed under the semitensor product and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> L methods. Finally, the viability of the results in the article is shown by considering a 12-gene hepatocellular cancer cell tumor network.