Real-Time State Reconstruction in a Single-Transistor Chaotic Oscillator Using a Microcontroller-Based Digital Model

In this work, we address the problem of reconstructing the complete state variables of a chaotic circuit by developing its digital model. In particular, the reconstruction methodology leverages the synchronization between the analog circuit and its digital counterpart, enabling the digital replica to track the chaotic motion of the physical entity. As a case study, we consider an atypical electronic oscillator based on a single transistor and demonstrate that all its state variables can be reconstructed in real time with reasonable accuracy using a simplified digital model implemented on an embedded microcontroller. Despite the use of an approximate equation system, simplified for computational reasons, and minimal state measurements, our results indicate that even a moderate level of synchronization is sufficient for reconstruction, highlighting the robustness of the presented method to model simplifications, component nonidealities, and noise. Given the severe information constraints in real-world scenarios, particularly for telemetry, the proposed approach appears especially useful toward extracting information from scalar time series, obtaining an approximation of a complete observation of the system state. It is also relevant to developing digital models when the governing equations of the system are still not fully established, as well as supporting the interaction between physical and cybernetic systems.