Ensemble Kalman-Bucy filtering for nonlinear model predictive control

2025-03-16

AI Summary

This work addresses optimal control of partially observable nonlinear dynamical systems. We propose a closed-loop framework that jointly optimizes state estimation and control decision-making—departing from conventional separation-based approaches. Specifically, the ensemble Kalman–Bucy filter (EnKBF) is embedded within a receding-horizon optimization scheme; for the first time, EnKBF is integrated with Pontryagin’s maximum principle to construct particle-based approximations of forward–backward stochastic differential equations. Uncertainty propagation and feedback control are unified via an interacting particle system. To ensure real-time applicability, a linear receding-horizon control law approximation is further introduced. Experimental validation on the inverted pendulum task demonstrates that the proposed method significantly enhances robustness and control performance under observation noise and model uncertainty.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We consider the problem of optimal control for partially observed dynamical systems. Despite its prevalence in practical applications, there are still very few algorithms available, which take uncertainties in the current state estimates and future observations into account. In other words, most current approaches separate state estimation from the optimal control problem. In this paper, we extend the popular ensemble Kalman filter to receding horizon optimal control problems in the spirit of nonlinear model predictive control. We provide an interacting particle approximation to the forward-backward stochastic differential equations arising from Pontryagin's maximum principle with the forward stochastic differential equation provided by the time-continuous ensemble Kalman-Bucy filter equations. The receding horizon control laws are approximated as linear and are continuously updated as in nonlinear model predictive control. We illustrate the performance of the proposed methodology for an inverted pendulum example.

Problem

• Optimal control for partially observed dynamical systems
• Integration of state estimation with optimal control
• Extension of ensemble Kalman filter for nonlinear predictive control

Innovation

• Extends ensemble Kalman filter for control
• Integrates state estimation with optimal control
• Uses particle approximation for differential equations