Dual Control of Linear Systems from Bilinear Observations with Belief Space Model Predictive Control

TL;DR

This paper introduces a belief-space model predictive control method for linear systems with bilinear observations, addressing challenges where control inputs influence state estimation quality.

Contribution

It proposes a novel B-MPC approach that plans over both state estimates and error covariances, improving control in bilinear observation settings.

Findings

B-MPC outperforms traditional controllers in synthetic experiments.

Lower estimation covariance achieved with B-MPC.

More uncertainty-aware actions are generated by B-MPC.

Abstract

We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observations of the state. In this setting, the separation principle can fail because control inputs influence the future quality of state estimates. State estimation requires an input-dependent Kalman filter whose gain and error covariance evolve as functions of the control inputs. To address this challenge, we propose a belief-space model predictive control ($\texttt{B-MPC}$) method that plans directly over both the estimated state and its error covariance. In particular, $\texttt{B-MPC}$ plans with a deterministic surrogate of the belief evolution defined by the input-dependent Kalman filter. Through numerical experiments in two synthetic settings, we show that $\texttt{B-MPC}$ can outperform both the separation-principle controller and its MPC variant in favorable regimes, and that these gains are accompanied by lower estimation covariance and more uncertainty-aware action choices.