A Dual Ensemble Kalman Filter Approach to Robust Control of Nonlinear Systems: An Application to Partial Differential Equations

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Abstract

This paper considers the problem of data-driven robust control design for nonlinear systems, for instance, obtained when discretizing nonlinear partial differential equations (PDEs). A robust learning control approach is developed for nonlinear affine in control systems based on Lyapunov redesign technique. The robust control is developed as a sum of an optimal learning control which stabilizes the system in absence of disturbances, and an additive Lyapunov-based robustification term which handles the effects of disturbances. The dual ensemble Kalman filter (dual EnKF) algorithm is utilized in the optimal control design methodology. A simulation study is done on the heat equation and Burgers partial differential equation.

Citation

@misc{joshi2025dualensemblekalmanfilter,
      title={A Dual Ensemble Kalman Filter Approach to Robust Control of Nonlinear Systems: An Application to Partial Differential Equations}, 
      author={Anant A. Joshi and Saviz Mowlavi and Mouhacine Benosman},
      year={2025},
      eprint={2508.21684},
      archivePrefix={arXiv},
      primaryClass={math.OC},
      url={https://arxiv.org/abs/2508.21684}, 
abstract={This paper considers the problem of data-driven robust control design 
for nonlinear systems, for instance, obtained when discretizing 
nonlinear partial differential equations (PDEs). A robust learning 
control approach is developed for nonlinear affine in control systems 
based on Lyapunov redesign technique. The robust control is developed as
 a sum of an optimal learning control which stabilizes the system in 
absence of disturbances, and an additive Lyapunov-based robustification 
term which handles the effects of disturbances. The dual ensemble Kalman
 filter (dual EnKF) algorithm is utilized in the optimal control design 
methodology. A simulation study is done on the heat equation and Burgers
 partial differential equation.
    },
}