Ensemble Kalman-Bucy filtering for nonlinear model predictive control
This addresses a gap in algorithms for control under uncertainty, which is incremental as it builds on existing ensemble Kalman filter and model predictive control methods.
The paper tackles the problem of optimal control for partially observed dynamical systems by extending the ensemble Kalman filter to receding horizon optimal control, integrating state estimation with control, and demonstrates performance on an inverted pendulum example.
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.