Belief-Informed Hybrid Control with Almost-Sure Target-Set Convergence

2026-10-05

AI Summary

This study addresses the control challenge of hybrid systems under parametric uncertainty, where exploratory deviations from a target set are required. It proposes a belief-driven dual control algorithm that integrates belief-space receding-horizon optimization with progress function constraints. A scalar state is introduced to bound cumulative relaxation, accommodating exploration-induced deviations, while parameter beliefs are updated via two-step lookahead and upper confidence bounds are expanded. The authors rigorously establish almost-sure convergence under recursive feasibility, along with bounds on neighborhood entry time. Experiments demonstrate that in a planar regulation task, the error decreases below 0.01 within 11 steps. For a bimanual assembly task, relative position errors are reduced by 96.4% compared to baselines, and empty feasible sets are successfully detected.

Abstract

Controlling a hybrid system to a target set under parameter uncertainty can require informative actions that temporarily drive the system state away from the specified set. We propose a belief-informed dual-control algorithm that combines belief-space receding-horizon selection with an expected-decrease constraint on a nonnegative target-set progress function. To accommodate exploratory deviations, a scalar controller state bounds the constraint's cumulative slack. Our algorithm's two-step lookahead selection uses predicted observations to update the parameter belief before evaluating the subsequent action's admissibility. Under distance-comparison bounds, correct conditional prediction, and recursive feasibility, we prove almost-sure target-set convergence at decision times and bound both the sum of expected progress-function values and the expected neighborhood-entry time. Upper confidence bounds extend these convergence guarantees to bounded model samples with summable error probabilities. In planar regulation with an unknown control direction, we verify recursive feasibility: the proposed two-step selection reduces the Euclidean state norm below 0.01 within 11 decisions for either sign, whereas a myopic one-step selection loses admissibility immediately after zero input. In a simulated bimanual assembly task, our algorithm's one-step implementation uses clearance feedback to complete the assembly under nominal friction, yielding a 96.4% lower infinity-norm relative-position error than the reference-tracking baseline at the method's completion time. At lower friction, its posterior conditioning successfully detects an empty admissible set, whereas a fixed-prior alternative admits an action that violates the conditional decrease constraint. Project page: https://clintonenwerem.com/belief-hybrid-control/.

Problem

• hybrid system control
• parameter uncertainty
• target-set convergence
• dual control
• belief space

Innovation

• dual control
• belief-space planning
• hybrid systems
• almost-sure convergence
• receding-horizon control