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A Control-Theoretic Foundation for Agentic Systems

Ali Eslami, Jiangbo Yu

TL;DR

A control-theoretic framework for analyzing agentic systems embedded within feedback control loops and shows that increasing agency introduces dynamical mechanisms including time-varying adaptation, endogenous switching, decision-induced delays, and structural reconfiguration of the control pipeline.

Abstract

This paper develops a control-theoretic framework for analyzing agentic systems embedded within feedback control loops. In such systems, an AI agent may adapt controller parameters, select among control strategies, invoke tools, reconfigure decision architectures, or modify control objectives during operation. We formalize these capabilities by interpreting agency as hierarchical decision authority over the control architecture. A unified dynamical representation is introduced that incorporates memory, learning, tool activation, interaction signals, and goal descriptors within a single closed-loop structure. Based on this representation, we define a five-level hierarchy of agency ranging from reactive rule-based control to the synthesis of control objectives and controller architectures. The framework is presented in both nonlinear and linear settings, allowing agentic behaviors to be interpreted using standard control-theoretic constructs such as feedback gains, switching signals, parameter adaptation laws, and quadratic cost functions. The analysis shows that increasing agency introduces dynamical mechanisms including time-varying adaptation, endogenous switching, decision-induced delays, and structural reconfiguration of the control pipeline. This perspective provides a mathematical foundation for analyzing stability, safety, and performance of AI-enabled control systems.

A Control-Theoretic Foundation for Agentic Systems

TL;DR

A control-theoretic framework for analyzing agentic systems embedded within feedback control loops and shows that increasing agency introduces dynamical mechanisms including time-varying adaptation, endogenous switching, decision-induced delays, and structural reconfiguration of the control pipeline.

Abstract

This paper develops a control-theoretic framework for analyzing agentic systems embedded within feedback control loops. In such systems, an AI agent may adapt controller parameters, select among control strategies, invoke tools, reconfigure decision architectures, or modify control objectives during operation. We formalize these capabilities by interpreting agency as hierarchical decision authority over the control architecture. A unified dynamical representation is introduced that incorporates memory, learning, tool activation, interaction signals, and goal descriptors within a single closed-loop structure. Based on this representation, we define a five-level hierarchy of agency ranging from reactive rule-based control to the synthesis of control objectives and controller architectures. The framework is presented in both nonlinear and linear settings, allowing agentic behaviors to be interpreted using standard control-theoretic constructs such as feedback gains, switching signals, parameter adaptation laws, and quadratic cost functions. The analysis shows that increasing agency introduces dynamical mechanisms including time-varying adaptation, endogenous switching, decision-induced delays, and structural reconfiguration of the control pipeline. This perspective provides a mathematical foundation for analyzing stability, safety, and performance of AI-enabled control systems.
Paper Structure (43 sections, 98 equations, 5 figures)

This paper contains 43 sections, 98 equations, 5 figures.

Table of Contents

  1. INTRODUCTION
  2. Problem Formulation and Unified Agentic Control Architecture
  3. Information Set and Internal Variables
  4. Tool-Augmented Decision Architecture
  5. Goal Representation
  6. Learning and Adaptation
  7. Unified Agentic Controller
  8. Interpretation
  9. Agency Levels as Hierarchical Control Authority
  10. Level 1: Reactive Rule-Based Agency
  11. Level 2: Adaptive Agency Within a Fixed Structure
  12. Level 3: Strategic Agency Through Selection Among Predefined Alternatives
  13. Level 4: Structural Agency Through Tool Composition and Architecture Reconfiguration
  14. Level 5: Generative Agency Under Governance Constraints
  15. Summary of the Hierarchy
  16. ...and 28 more sections

Figures (5)

  • Figure 1: Five-level hierarchy of agency in AI-enabled control systems. Increasing agency corresponds to increasing decision authority over the control architecture: from reactive rule-based control (Level 1), to adaptive parameter tuning (Level 2), strategic selection among predefined controllers and objectives (Level 3), structural reconfiguration through modular workflow composition (Level 4), and generative synthesis of goals and architectures under governance constraints (Level 5).
  • Figure 2: Closed-loop response of the spring–mass–damper system under adaptive proportional gain. A slow adaptation rate maintains stability.
  • Figure 3: State trajectories fast adaptation rates, destabilizing the time-varying closed-loop system.
  • Figure 4: Illustration of how fast switchings between control architectures lead to instability.
  • Figure 5: State trajectories and state norms under short ($d=1$) and long ($d=8$) dwell-time switching between two control pipelines. Longer activation of the estimator-augmented pipeline leads to significantly larger state growth due to the internal dynamics introduced by the additional modules.