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

2026-04-27

AI Summary

This work addresses the challenge posed by bilinear observations in linear systems, where control inputs simultaneously influence both state dynamics and observation quality, thereby invalidating the classical separation principle. To overcome this limitation, the paper proposes Belief-space Model Predictive Control (B-MPC), which directly plans in the belief space defined by the estimated state and its error covariance. B-MPC leverages a deterministic surrogate model of belief evolution derived from an input-dependent Kalman filter to jointly optimize state estimation and control policies, explicitly accounting for the active effect of control actions on observation uncertainty. Experimental results on two synthetic tasks demonstrate that B-MPC outperforms controllers based on the separation principle and their MPC variants, achieving lower estimation covariance and generating control actions that are more aware of uncertainty.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• bilinear observations
• linear systems
• state estimation
• separation principle
• control input

Innovation

• belief-space MPC
• bilinear observations
• input-dependent Kalman filter
• separation principle failure
• covariance-aware control