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

## TL;DR

This paper introduces a dual ensemble Kalman filter-based robust control method for nonlinear PDEs, combining optimal learning control with Lyapunov-based robustification, demonstrated on heat and Burgers equations.

## Contribution

It develops a novel dual EnKF approach integrated with Lyapunov redesign for robust control of nonlinear PDE discretizations.

## Key findings

- Effective stabilization of nonlinear PDEs demonstrated in simulations.
- Dual EnKF enhances robustness against disturbances.
- Method applicable to various nonlinear PDE control problems.

## 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.