arXiv subjects

Yunxiao Ren

Publications and source records attributed to Yunxiao Ren.

8 recordsLinked to original sources

arXiv2026

Optimality Robustness in Koopman-Based Control

The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This naturally raises the question of how such uncertainty-induced optimality deviation can be quantified and mitigated. To address this problem, we adopt a unified analysis-to-design perspective that connects the characterization of optimality robustness with its improvement through controller design. At the analysis level, we establish a unified treatment of multiple uncertainty sources in Koopman-based control, where approximation error and noisy data are incorporated into a common robustness analysis through a norm-bounded representation. At the design level, we develop a robustness-aware optimal control methodology that provably reduces such optimality deviations, thereby enhancing robustness while explicitly revealing a quantitative trade-off between nominal optimality and robustness. As for practical implementation aspect, we further propose a tractable policy iteration algorithm, whose well-posedness and convergence are established via vanishing viscosity regularization and elliptic partial differential equation (PDE) techniques. Numerical examples validate the theoretical findings and demonstrate the effectiveness of proposed methodology.

eess.SY↗

arXiv2026

Optimality Deviation using the Koopman Operator

This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics through a lifted state space, the presence of approximation error inevitably leads to deviations in the computed optimal controller and the resulting value function. We derive explicit upper bounds for these optimality deviations, which characterize the worst-case effect of approximation error. Supported by numerical examples, these theoretical findings provide a quantitative foundation for improving the robustness of data-driven optimal controller design.

math.OC↗

arXiv2026

Turbulence Physics Governs a Scaling Law for the Machine-Learning Predictability Ceiling in Chaotic Flow

For centuries, the intrinsic chaos of unsteady fluid motion has stood as a formidable barrier to long-term forecasting. While machine learning (ML) has recently emerged as a transformative paradigm for predicting flow evolution, it encounters a pervasive yet unexplained "performance wall": an inevitable deterioration in accuracy as the forecast horizon extends. Here, we demonstrate that this deterioration is not a deficiency of model architecture, no matter how state-of-the-art, but a fundamental constraint imposed by the underlying system, which can be understood through turbulence theory established decades ago. In the setting of bluff body flow, a canonical phenomenon for spatiotemporal complexity in fluid mechanics, we reveal a scaling law governing the deterioration of ML predictability, derived from a Kolmogorov-inspired framework and validated through high-fidelity simulations. Our findings establish a closed loop between the predictability ceiling and its interpretation, bridging the gap between transparent physical theories and modern black-box inference. More broadly, this work provides a theoretical compass for constructing trustworthy ML in complex dynamical systems across the physical sciences.

physics.flu-dyn↗

arXiv2026

Coalitional Zero-Sum Games for ${H_{\infty}}$ Leader-Following Consensus Control

This paper investigates the leader-following consensus problem for a class of multi-agent systems subject to adversarial attack-like external inputs. To address this, we formulate the robust leader-following control problem as a global coalitional min-max zero-sum game using differential game theory. Specifically, the agents' control inputs form a coalition to minimize a global cost function, while the attacks form an opposing coalition to maximize it. Notably, when these external adversarial attacks manifest as disturbances, the designed game-theoretic control policy systematically yields a robust $H_\infty$ control law. Addressing this problem inherently requires solving a high-dimensional generalized algebraic Riccati equation (GARE), which poses significant challenges for distributed computation and controller implementation. To overcome these challenges, we propose a two-fold approach. First, a decentralized computational strategy is devised to decompose the high-dimensional GARE into multiple uniform, lower-dimensional GAREs. Second, a dynamic average consensus-based decoupling algorithm is developed to resolve the inherent coupling structure of the robust control law, thereby facilitating its distributed implementation. Finally, numerical simulations on the formation control of multi-vehicle systems with feedback-linearized dynamics are conducted to validate the effectiveness of the proposed algorithms.

eess.SY↗

arXiv2026

Deep Koopman Iterative Learning and Stability-Guaranteed Control for Unknown Nonlinear Time-Varying Systems

This paper proposes a Koopman-based framework for modeling, prediction, and control of unknown nonlinear time-varying systems. We present a novel Koopman-based learning method for predicting the state of unknown nonlinear time-varying systems, upon which a robust controller is designed to ensure that the resulting closed-loop system is input-to-state stable with respect to the Koopman approximation error. The error of the lifted system model learned through the Koopman-based method increases over time due to the time-varying nature of the nonlinear time-varying system. To address this issue, an online iterative update scheme is incorporated into the learning process to update the lifted system model, aligning it more precisely with the time-varying nonlinear system by integrating the updated data and discarding the outdated data. A necessary condition for the feasibility of the proposed iterative learning method is derived. In order to reduce unnecessary system updates while ensuring the prediction accuracy of the lifted system, the update mechanism is enhanced to determine whether to update the lifted system and meanwhile to reduce updates that deteriorate the fitting performance. Furthermore, based on the online-updated lifted system, a controller is designed to ensure the closed-loop controlled system be input-to-state stable with respect to the Koopman approximation error. Numerical simulations on the Duffing oscillator, the serial manipulator, and the synthetic biological network system are presented to demonstrate the effectiveness of the proposed method for the approximation and control of unknown nonlinear time-varying systems. The results show that the proposed approach outperforms existing methods in terms of approximation accuracy and computational efficiency, even under significant system variations.

eess.SY↗

arXiv2025

Integrating Uncertainties for Koopman-Based Stabilization

Over the past decades, the Koopman operator has been widely applied in data-driven control, yet its theoretical foundations remain underexplored. This paper establishes a unified framework to address the robust stabilization problem in data-driven control via the Koopman operator, fully accounting for three uncertainties: projection error, estimation error, and process disturbance. It comprehensively investigates both direct and indirect data-driven control approaches, facilitating flexible methodology selection for analysis and control. For the direct approach, considering process disturbances, the lifted-state feedback controller, designed via a linear matrix inequality (LMI), robustly stabilizes all lifted bilinear systems consistent with noisy data. For the indirect approach requiring system identification, the feedback controller, designed using a nonlinear matrix inequality convertible to an LMI, ensures closed-loop stability under worst-case process disturbances. Numerical simulations via cross-validation validate the effectiveness of both approaches, highlighting their theoretical significance and practical utility.

eess.SY↗

arXiv2025

Vortex-Induced Drag Forecast for Cylinder in Non-uniform Inflow

In this letter, a physics-based data-driven strategy is developed to predict vortex-induced drag on a circular cylinder under non-uniform inflow conditions - a prevalent issue for engineering applications at moderate Reynolds numbers. Traditional pressure-signal-based models exhibit limitations due to complex vortex dynamics coupled with non-uniform inflow. To address this issue, a modified fully connected neural network (FCNN) architecture is established that integrates upstream velocity measurements (serving as an inflow calibration) with pressure-signal-based inputs to enhance predictive capability (R^2 ~ 0 to 0.75). Direct numerical simulations (DNS) at Reynolds number Re = 4000 are implemented for model training and validation. Iterative optimizations are conducted to derive optimized input configurations of pressure sensor placements and velocity components at upstream locations. The optimized model achieves an R^2 score of 0.75 in forecasting high-amplitude drag coefficient fluctuations (C_d=0.2 - 1.2) within a future time window of one time unit. An exponential scaling between model performance and optimized pressure signal inputs is observed, and the predictive capability of sparsely distributed but optimized sensors is interpreted by the scaling. The optimized sensor placements correspond to the physical mechanism that the flow separation dynamics play a governing role in vortex-induced drag generation. This work advances machine learning applications in fluid-structure interaction systems, offering a scalable strategy for forecasting statistics in turbulent flows under real-world engineering conditions.

physics.flu-dyn↗

arXiv2024

On the Effects and Optimal Design of Redundant Sensors in Collaborative State Estimation

The existence of redundant sensors in collaborative state estimation is a common occurrence, yet their true significance remains elusive. This paper comprehensively investigates the effects and optimal design of redundant sensors in sensor networks that use Kalman filtering to estimate the state of a random process collaboratively. The paper presents two main results: a theoretical analysis of the effects of redundant sensors and an engineering-oriented optimal design of redundant sensors. In the theoretical analysis, the paper leverages Riccati equations and Symplectic matrix theory to unveil the explicit role of redundant sensors in cooperative state estimation. The results unequivocally demonstrate that the addition of redundant sensors enhances the estimation performance of the sensor network, aligning with the principle of ``more is better". Moreover, the paper establishes a precise sufficient and necessary condition to assess whether the inclusion of redundant sensors improves the overall estimation performance. Moving towards engineering-oriented design optimization, the paper proposes a novel algorithm to tackle the optimal design problem of redundant sensors, and the convergence of the proposed algorithm is guaranteed. Numerical simulations are provided to demonstrate the results.

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