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A New Approach to Controlling Linear Dynamical Systems

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Online Convex OptimizationOnline ControlLinear Dynamical Systems
Abstract:

We propose a new method for controlling linear dynamical systems under adversarial disturbances and cost functions. Our algorithm achieves a running time that scales polylogarithmically with the inverse of the stability margin, improving upon prior methods with polynomial dependence maintaining the same regret guarantees. The technique, which may be of independent interest, is based on a novel convex relaxation that approximates linear control policies using spectral filters constructed from the eigenvectors of a specific Hankel matrix.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper proposes an online control algorithm for linear dynamical systems under adversarial disturbances, achieving polylogarithmic runtime dependence on the stability margin while maintaining existing regret guarantees. It resides in the Single-Agent Online Control leaf, which contains five papers total including this work. This leaf sits within the broader Online Control and Regret Minimization branch, indicating a moderately populated research direction focused on sequential decision-making with adversarial perturbations. The taxonomy shows this is an active but not overcrowded area, with sibling papers pursuing related regret-minimization objectives under various structural assumptions.

The taxonomy reveals neighboring research directions that provide context for this work. The Multi-Agent Distributed Online Control leaf addresses network settings with local observations, while Online Control with Predictions or Memory explores lookahead mechanisms to improve performance. The Safety-Critical and Constrained Control branch tackles hard constraints under disturbances, and Robust Control Synthesis and Optimization develops systematic design methods including H-infinity approaches. The paper's focus on computational efficiency in single-agent settings distinguishes it from these neighboring directions, though connections exist through shared tools like convex optimization and spectral methods used across multiple branches.

Among sixteen candidates examined across three contributions, the spectral representation algorithm and runtime improvement show no clear refutation, while the Hankel-based convex relaxation technique has two potentially overlapping prior works among eight candidates examined. The limited search scope means these statistics reflect top semantic matches rather than exhaustive coverage. The runtime improvement contribution appears particularly novel within the examined set, with no candidates among two examined providing comparable polylogarithmic scaling. The spectral filter relaxation, despite two refutable candidates, may still offer distinct technical innovations not fully captured by semantic similarity alone.

Based on the limited literature search examining sixteen candidates, the work appears to make substantive contributions to computational efficiency in online control, though the Hankel-based relaxation technique has some prior overlap. The taxonomy position in a moderately populated leaf suggests room for innovation, particularly in algorithmic techniques that improve scaling properties. A more comprehensive search beyond top semantic matches would be needed to definitively assess novelty across all three contributions, especially regarding the spectral filter construction methodology.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
16
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: controlling linear dynamical systems under adversarial disturbances. The field addresses how to design controllers that maintain performance guarantees when facing worst-case or non-stochastic perturbations, rather than relying on statistical assumptions. The taxonomy reveals several complementary perspectives: Online Control and Regret Minimization focuses on sequential decision-making with performance measured against optimal hindsight policies, often drawing on tools from online learning; Safety-Critical and Constrained Control emphasizes maintaining invariants and hard constraints despite disturbances; Robust Control Synthesis and Optimization develops systematic design methods ensuring stability and performance under bounded uncertainties; System Identification and Estimation Under Attacks studies how to learn system dynamics when measurements or inputs may be corrupted; Neural Network Control and Verification explores data-driven controllers with formal guarantees; Reinforcement Learning and Adversarial Training blends adaptive learning with robustness; Specialized Control Architectures and Applications targets domain-specific challenges; and Continuous-Time Online Control extends discrete-time regret frameworks to differential equations. Works such as Online Adversarial Control[1] and Black-box Control[8] illustrate how online learning principles apply to control, while Observability Under Attacks[4] and Secure Cyber-Physical Systems[6] highlight security-oriented perspectives. Within the Online Control and Regret Minimization branch, a central theme is balancing exploration, exploitation, and robustness in sequential settings. Single-agent methods like Controlling Linear Systems[0] aim to minimize regret against adversarial disturbances, closely related to Online Adversarial Control[1] and Logarithmic Regret[29], which pursue tighter bounds under various structural assumptions. Black-box Control[8] and Improper Learning Control[45] explore settings with limited model knowledge, trading off sample complexity and robustness. In contrast, works like Online Optimal Tracking[3] incorporate reference-tracking objectives, and Multi-Agent Adversarial Control[5] extends the framework to distributed settings. Controlling Linear Systems[0] fits naturally among these single-agent regret-minimization efforts, sharing the goal of provable performance under worst-case disturbances but potentially differing in assumptions about system observability or disturbance structure compared to neighbors like Logarithmic Regret[29] or Black-box Control[8]. Open questions persist around the tightest achievable regret rates, the role of partial observability, and how to incorporate safety constraints without sacrificing learning efficiency.

Claimed Contributions

Online Spectral Control (OSC) algorithm with spectral representation

The authors propose a new control algorithm that uses spectral filters constructed from eigenvectors of a Hankel matrix to compress disturbance history into compact features. This spectral representation provides a universal feature map that reduces online control to regression on low-dimensional spectral features.

6 retrieved papers
Exponential runtime improvement with polylogarithmic dependence on stability margin

The method achieves runtime that scales as O(log^4(T/γ)) per step, exponentially faster than prior polynomial-time methods, while maintaining regret bound of Õ(γ^{-4}√T). This is accomplished through efficient online convolution techniques applied to spectral features.

2 retrieved papers
Novel convex relaxation for linear control policies using Hankel-based spectral filters

The authors develop a new convex relaxation technique that approximates the class of diagonalizably stable linear policies using spectral controllers. The filters are derived from a Hankel matrix with entries (1-γ)^{i+j-1}/(i+j-1), providing a convex policy class for efficient learning.

8 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Online Spectral Control (OSC) algorithm with spectral representation

The authors propose a new control algorithm that uses spectral filters constructed from eigenvectors of a Hankel matrix to compress disturbance history into compact features. This spectral representation provides a universal feature map that reduces online control to regression on low-dimensional spectral features.

Contribution

Exponential runtime improvement with polylogarithmic dependence on stability margin

The method achieves runtime that scales as O(log^4(T/γ)) per step, exponentially faster than prior polynomial-time methods, while maintaining regret bound of Õ(γ^{-4}√T). This is accomplished through efficient online convolution techniques applied to spectral features.

Contribution

Novel convex relaxation for linear control policies using Hankel-based spectral filters

The authors develop a new convex relaxation technique that approximates the class of diagonalizably stable linear policies using spectral controllers. The filters are derived from a Hankel matrix with entries (1-γ)^{i+j-1}/(i+j-1), providing a convex policy class for efficient learning.

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