Dual Control of Linear Systems from Bilinear Observations with Belief Space Model Predictive Control
For control of systems with input-dependent observations, this work provides a method that improves over separation-based approaches, though results are limited to synthetic settings.
This paper addresses finite-horizon quadratic control of linear systems with bilinear observations, where control inputs affect both state dynamics and observation quality. The proposed belief-space model predictive control (B-MPC) method outperforms separation-principle controllers in numerical experiments, achieving lower estimation covariance and more uncertainty-aware actions.
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.