Report on Recent Developments in Data-Driven Control and Uncertainty Quantification

General Direction of the Field

The recent advancements in the field of data-driven control and uncertainty quantification are pushing the boundaries of traditional control theory, particularly in the context of nonlinear and stochastic systems. The focus is shifting towards developing robust, adaptive, and resilient control strategies that can operate effectively even when the system dynamics are unknown or subject to significant disturbances.

One of the key trends is the integration of advanced mathematical tools, such as the signature transform, into control design. This approach allows for the rigorous representation and prediction of system trajectories, enabling the development of novel control strategies that are data-driven and predictive in nature. The signature transform, in particular, is emerging as a powerful feature extraction method for continuous-time, input-affine systems, offering a promising avenue for future research in this area.

Another significant development is the move towards distributionally robust control methods. These methods are designed to handle uncertainties in both the system dynamics and the noise distributions, providing a more flexible and reliable framework for predictive control. The incorporation of conditional value-at-risk and other risk measures into the control design process is enhancing the robustness of these methods, making them suitable for real-world applications where safety constraints are critical.

Uncertainty quantification is also gaining traction, with a particular emphasis on distinguishing between aleatoric (stochastic) and epistemic (data-driven) uncertainties. Recent work has introduced novel calibration techniques that can account for both types of uncertainty in a theoretically grounded manner, leading to more accurate and reliable predictions of system behavior. These methods are particularly useful for planning and decision-making in environments where the dynamics are subject to significant changes.

Lastly, there is a growing interest in developing resilient control strategies that can withstand cyber-attacks, such as denial-of-service (DoS) attacks. The focus here is on ensuring the stability and performance of the control system even under adverse conditions, with recent research demonstrating the effectiveness of reinforcement learning-based approaches in achieving this goal.

Noteworthy Papers

• Data-driven control of input-affine systems: the role of the signature transform.
  This paper introduces a novel signature-based control strategy that leverages the signature transform for predictive control, offering a promising direction for future research in data-driven control.

• Distributionally Robust Stochastic Data-Driven Predictive Control with Optimized Feedback Gain.
  The paper presents a distributionally robust control method that optimizes feedback gain and handles non-Gaussian noise, demonstrating enhanced performance over previous designs.

• Quantifying Aleatoric and Epistemic Dynamics Uncertainty via Local Conformal Calibration.
  This work introduces a new approach to quantifying both aleatoric and epistemic uncertainties in dynamics models, providing a theoretically grounded method for uncertainty calibration.

• Resilient Learning-Based Control Under Denial-of-Service Attacks.
  The paper proposes a resilient reinforcement learning method that ensures stability under DoS attacks, demonstrating its effectiveness in a practical control scenario.