Observer-based output tracking for asynchronous boolean control networks under noise

A critical problem in regulating genetic networks is the output tracking of Boolean Control Networks (BCNs). This is because implementing BCNs is affected by dual uncertainty originating from the inherent stochasticity of asynchronous updates and the observational ambiguity introduced by output measurement noise. Driven by these challenges, this paper introduces a unified probabilistic control framework that shifts the paradigm from deterministic state estimation to a belief state representation. Specifically, a belief-state observer is developed utilizing the semi-tensor product and recursive Bayesian inference. This observer reconstructs the full posterior probability distribution over network states, discarding output measurement noise and resolving hidden-state ambiguities. Building upon the estimated belief states, a belief-based Model Predictive Control strategy is introduced to generate optimal control sequences for robust output tracking. Furthermore, rigorous theoretical analysis using the stochastic Lyapunov method guarantees the mean-square boundedness and stability of the closed-loop system. Finally, the efficacy and robustness of the proposed method are validated through numerical studies on two distinct biological regulatory networks.