Reconstructibility and observers of mix‐valued logical control networks

Abstract This research investigates reconstructibility analysis and observer design for mix‐valued logical control networks through the application of the semi‐tensor product. First, recursive and explicit methods are proposed for reconstructibility, along with a termination criterion aimed at enhancing the runtime efficiency of the recursive method. Then, shift‐register and Luenberger‐like observers are given for reconstructible mix‐valued logical control networks. The former provides accurate state estimation after reaching the minimal reconstructibility index, while the latter ensures that the state estimation consistently encompasses the true state and converges within a time frame that does not exceed the minimum reconstructibility index. Finally, an oxidative stress response pathway in biological systems is modeled to validate our methods. This demonstrates their capability to estimate internal states that are critical for understanding system behavior but often impossible to measure directly in real‐time, enabling applications like fault detection in biological processes.