In a recent study published in the journal Nature Communications, researchers introduced an innovative machine learning (ML) algorithm capable of controlling chaotic systems to arbitrary states using low-power embedded computing hardware. Their technique showcased the ability to stabilize a chaotic electronic circuit to desired states and trajectories by employing a data-driven nonlinear controller implemented on a field-programmable gate array (FPGA).
More negative means less information is contained in the features. The red circles are the features used in the model, and the black xs are excluded. Image Credit: https://www.nature.com/articles/s41467-024-48133-3
Background
Chaotic systems are nonlinear dynamical systems known for their complex and unpredictable behavior due to their sensitivity to initial conditions. Controlling these systems is a challenging task and typically requires a precise mathematical model or thorough system characterization for adjusting controller parameters. Traditional control methods often assume linear system responses, limiting their effectiveness with nonlinear and chaotic systems.
ML offers a data-driven alternative by creating a digital twin of the system's predictive digital model. An accurate digital twin can facilitate various applications, including autonomous system control. However, existing ML solutions can be costly and reliant on computational engines like power-intensive graphical processors. Alternatively, custom neuromorphic chips leveraging analog-digital designs or advanced materials may provide low-power operation solutions.
About the Research
In this article, the authors utilized a next-generation reservoir computing (NG-RC) algorithm, an advanced ML technique tailored for learning dynamical systems, to design a nonlinear controller for a chaotic system. The NG-RC algorithm offers several advantages over other ML algorithms, including fewer parameters to optimize, reduced training data requirements, and lower computational overhead. Moreover, it can adaptively learn the non-linear characteristics of the system independently from data, allowing it to readjust to system degradation or damaging events over time.
The chaotic system under investigation comprises an electronic circuit composed of passive components and an active negative resistor capable of exhibiting autonomous double-scroll chaotic dynamics. To control this system, the researchers measured two accessible variables including voltages across two capacitors and manipulated one of them by injecting a control current into the circuit. The control current was determined by a nonlinear control law leveraging the NG-RC algorithm to predict the system's future state and counteract its nonlinear dynamical evolution.
To implement the NG-RC algorithm and the control law, the authors utilized an FPGA, a type of reconfigurable hardware renowned for its parallel computing capabilities and co-located memory with processing logic gates. This architecture enhances efficiency and reduces power consumption. The FPGA was employed to gather real-time data from the circuit, process it using firmware-based NG-RC, and execute the control perturbations.
Research Findings
The paper showcased that the NG-RC-based controller effectively stabilized the dynamics of the chaotic circuit to trajectories that were unattainable for conventional chaos control methods like the Ott-Grebogi-Yorke (OGY) and Pyragas methods. These traditional methods were limited to stabilizing unstable states within the dynamics and making minor adjustments to system parameters.
In contrast, the NG-RC-based controller demonstrated the ability to stabilize the system to various unstable steady states, including those at the origin and within the scrolls, and to swiftly switch between them, as well as to a random trajectory.
Furthermore, the authors compared the performance of the NG-RC-based controller to that of a simple linear proportional feedback controller. They found that the NG-RC-based controller excelled in every task except when stabilizing the system at nonzero unstable steady states, where the dynamics approximated linearity. The NG-RC-based controller achieved a 1.7 times smaller error on the most difficult control task of following a random waveform, requiring only a small increase in the percentage of available FPGA resources and power consumption.
The researchers further analyzed the stability of the nonlinear controller concerning feedback gain and control-loop latency. They discovered a broad range of feedback gains conducive to high-quality control, with minimal control perturbations observed at unstable steady states, demonstrating the robustness of the approach. Additionally, they reported the power consumption and energy per inference of the controller, noting that the NG-RC algorithm exhibited significantly lower energy consumption (25.0±7.0 nJ per inference) compared to other ML-based controllers.
Conclusion
In summary, the researchers provided a proof-of-concept demonstration of utilizing a cutting-edge ML algorithm to monitor complex systems deployed on a small and low-power computing device. They illustrated the robustness of the controller to modeling and discretization errors, delays, and noise.
Furthermore, they proposed potential applications of their approach in controlling other chaotic systems, such as lasers, fluid dynamics, and biological systems. They highlighted the possibility of employing this technique in various new applications, including controlling autonomous systems, optimizing system design, and monitoring system health.
Additionally, the researchers suggested several directions for future work. They proposed exploring methods like performing training directly on the FPGA using online regularized regression. They also recommended extending the application of the controller to other problems, such as spatial-temporal dynamics. Moreover, they emphasized the importance of reducing power consumption to sub-mW levels, which could be achieved through the use of more power-efficient FPGAs or custom application-specific integrated circuits.
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