Time-Optimal Stabilization of Asynchronous Boolean Control Networks Under State and Control Constraints

This paper investigates the problem of time-optimal stabilization in Boolean control networks (BCNs) with an asynchronous update scheme, subject to state and control constraints. BCNs are fundamental models for various applications, including biological regulatory systems. While asynchronous updates provide a more realistic representation, they introduce nondeterministic state transitions, posing significant challenges for control strategy design. We propose a systematic approach based on an iterative algorithm that efficiently computes the basin of attraction (BoA) of a steady state and constructs a state feedback control law to ensure time-optimal stabilization from any initial state in the BoA to the steady state. The algorithm explicitly accounts for state and control constraints. The correctness and time complexity of the proposed approach are rigorously analyzed. Notably, the time complexity remains relatively low since our algorithm only requires one-step state transition computations, avoiding the expensive matrix products commonly used in existing algebraic methods. To validate our approach, we apply it to an asynchronous BCN model of the myeloid differentiation process involving 11 genes. The results demonstrate the effectiveness and efficiency of our method in the theoretical analysis and control of asynchronous BCNs particularly modelling gene regulatory systems. Our algorithm code is publicly accessible at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://gitee.com/shuhuagao/tos-abcn</uri>.