Dual Control of Linear Systems from Bilinear Observations with Belief Space Model Predictive Control
Daniel Cao, Beixi Du, Andrew Lowitt, Sunmook Choi, Sarah Dean + 1 more
TLDR
This paper introduces Belief-Space Model Predictive Control (B-MPC) for dual control of linear systems with bilinear observations, outperforming traditional methods.
Key contributions
- Addresses dual control in linear systems where inputs affect state dynamics and observation quality.
- Proposes Belief-Space Model Predictive Control (B-MPC) to plan over estimated state and its error covariance.
- Utilizes a deterministic surrogate of belief evolution from an input-dependent Kalman filter.
- Demonstrates B-MPC outperforms baselines, yielding lower estimation covariance and better actions.
Why it matters
This paper addresses a challenging dual control problem where inputs affect both system state and observation quality, causing the separation principle to fail. B-MPC offers a novel, effective solution that improves control performance and reduces estimation uncertainty. This is crucial for robust control in complex, uncertain environments.
Original 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.
📬 Weekly AI Paper Digest
Get the top 10 AI/ML arXiv papers from the week — summarized, scored, and delivered to your inbox every Monday.