Novel Online Learning Algorithm for Supervisory Switching Control in Linear Systems
Researchers have proposed a novel data-driven algorithm that adapts multi-armed bandit techniques to supervisory switching control for partially-observed linear dynamical systems. Classical supervisory control methods offer asymptotic stability but lack finite-time performance bounds, while existing non-asymptotic methods require assumptions—such as system stability—that are incompatible with testing potentially unstable controllers. The work provides dimension-free, finite-time guarantees, identifying the correct controller in O(N log² N) steps while maintaining finite L₂-gain against disturbances.
The paper, posted to arXiv and submitted across multiple revisions through June 2026, addresses a longstanding gap in control theory: supervisory switching control systems must select among N candidate controllers for an unknown dynamical system, but some candidates may destabilize the system. Classical estimator-based approaches guarantee asymptotic stability without quantitative finite-time bounds, while modern online learning and system identification methods typically assume the system is already stable—an assumption that precludes safely testing destabilizing controllers. To resolve this incompatibility, the authors adapt multi-armed bandit algorithms to the control-theoretic setting, introducing scoring criteria that exploit system observability to isolate the influence of state history. This design enables simultaneous detection of destabilizing controllers and accurate system identification. Two algorithmic variants are presented, both achieving dimension-free finite-time guarantees and finite L₂-gain with respect to external disturbances, with controller identification completing in O(N log² N) steps.
What's missing
The paper does not report empirical or simulation results validating the theoretical guarantees on concrete benchmark systems, leaving open questions about practical performance in realistic noise regimes. Applicability to nonlinear or time-varying systems is not addressed.
What different sources said
- arXiv cs.LGCenter
Online Learning for Supervisory Switching Control
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