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

arXiv: https://arxiv.org/abs/2604.24663 · HTML: https://mlsanity.com/paper/2604.24663/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 6 of 6)

- [Learning Linear Dynamics from Bilinear Observations](https://mlsanity.com/paper/2409.16499/) (2024)
- [Belief Space Planning: A Covariance Steering Approach](https://mlsanity.com/paper/2105.11092/) (2021)
- [Bilinear Data-Driven Min-Max MPC: Designing Rational Controllers via Sum-of-squares Optimization](https://mlsanity.com/paper/2504.04870/) (2025)
- [Sub-optimality of the Separation Principle for Quadratic Control from Bilinear Observations](https://mlsanity.com/paper/2504.11555/) (2025)
- [Explore-then-Commit for Nonstationary Linear Bandits with Latent Dynamics](https://mlsanity.com/paper/2510.16208/) (2025)
- [Optimal Sampling-based Motion Planning in Gaussian Belief Space for Minimum Sensing Navigation](https://mlsanity.com/paper/2306.00264/) (2023)

## Abstract (arXiv)

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 (textttB-MPC) method that plans directly over both the estimated state and its error covariance. In particular, textttB-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 textttB-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.