Structured Taxonomy of Control Policies

• Structured Taxonomy of Control Policies is a comprehensive framework that hierarchically classifies control strategies in fields such as economics, security, and robotics.
• It employs trait-based parametrization and formal mapping techniques to link high-level intentions with low-level operational commands.
• The approach enables standardized policy evaluation and complete coverage verification, ensuring interoperability across diverse system domains.

A structured taxonomy of control policies provides a hierarchical and formalized framework for classifying, designing, implementing, and analyzing intervention strategies governing complex systems—spanning economics, network security, AI governance, optimal control, and robotics. Taxonomies reveal the canonical levers available to agents or authorities, clarify granularity and mapping between high-level intent and low-level commands, and expose both algorithmic and regulatory implications for system design and evaluation. This article presents key models and taxonomies published in recent research and synthesizes major dimensions: control policy tree structures, information and data models, trait-based parametrization, geometric realization, RL-based classifications, and semantic mapping across domains.

1. Hierarchical Tree Structures and Economic Taxonomies

Hierarchical decomposition is central to exhaustive control policy taxonomies. In the economic sphere, the framework introduced by "Economic Policy Taxonomy" (Sadykhov et al., 4 Jul 2025) constructs a tree rooted at the generic concept of "Policy," branching into stabilization and international trade policies, and further specializing into fiscal, monetary, and auxiliary domains. Each subdomain, such as Fiscal Policy, is decomposed into atomic policy categories (e.g., tax revenue, expenditure, non-operating income), which are themselves taxonomized by traits—tractable parameters such as tax calculation type, rate, or payment size.

For example, tax revenue policy divides into income tax, property tax, sales tax, and Pigouvian tax, with further specialization and parametrization using formally defined traits: $$\text{Tax Calculation Type} : \{\text{Proportional}[\tau],\, \text{Progressive}[\{(\text{band}_j,r_j)\}]\}$$ Complete enumeration of category-trait pairs generates the set of atomic control variables for macro-micro simulators: $y = F(x, \text{initial conditions})$ with $x \in \mathbb{R}^{P}$ the full vector of atomic policy levers and $y$ the macroeconomic indicators.

2. Information, Data, and Capability Models in Security Policy Taxonomy

In network security, "A Formal Model of Security Controls' Capabilities" (Basile et al., 6 May 2024) presents the Security Capability Model (SCM), articulating an information model for control policies comprising:

• ConditionCapability (Cond): Typed predicates evaluated over packets, flows, or events, supporting operations such as exactMatch, prefixMatch, or regex.
• ActionCapability (Act): Atomic operations triggered by matched conditions—accept, drop, reject, encrypt, tunnel.
• EventCapability (Evt): Triggers on which rule sets are evaluated, such as packet arrival or session initiation.
• Rule: Tuple $(id, Ev, CondSet, ActSet, clause)$, evaluated via clause semantics (“ALL” for conjunctive, “ANY” for disjunctive matching).
• ResolutionStrategy: Specifies rule conflict resolution, e.g. FirstMatchingRule, DenyOverride.
• Policy: Defines target device, rule set, resolution strategy, and default action.

The data model further stratifies capabilities into:

Family	Conditions	Actions	Resolution
Packet-Filtering	IpSrc, IpDst, Proto, ports, flags, interfaces	Accept, Drop, Reject	FirstMatchingRule
App-Layer Filter	HTTP method, URL regex, header/mime types	PF-actions, log, count	FMR / custom
Channel Protection	Flow selectors	encryptTunnel, decryptTunnel	“ALL” (conjunctive)

Policy granularity spans high-level intent (ABAC), mid-level NSF-abstract (XML), to low-level vendor config (CLI/API).

3. Trait-Based Parametrization, Matrix Verification, and Policy Exhaustiveness

Trait-based parametrization, as in (Sadykhov et al., 4 Jul 2025), underpins exhaustive and standardized policy taxonomies. Each atomic policy is formed by pairing a category (e.g., income tax) with a trait (e.g., proportional rate), yielding a catalog of control actions: $$\text{Atomic Policy} = (\text{Category}, \text{Trait}, \text{Parameters})$$ Verification of completeness and standardization proceeds via a binary trait-category incidence matrix $M \in \{0,1\}^{N \times T}$, with connectivity and coverage validated using Euclidean distances and minimum spanning trees over the signal vectors $S_i \in \{0,1\}^T$.

This methodology generalizes across domains, enabling exhaustive mapping for power systems (tariff traits, generator setpoints), telecommunications (bandwidth caps), and autonomous vehicles (steering/braking parameters).

4. Geometric and Realization-Based Taxonomies in Optimal Control

In optimal control, taxonomy is realized in terms of feedback policy structure, parameter space geometry, and algorithmic landscape (Talebi et al., 6 Jun 2024):

• Static State-Feedback: $u_t = K x_t$, $K \in \mathbb{R}^{m \times n}$. Stabilizing set $S = \{ K : \rho(A + BK) < 1 \}$ is open, contractible.
• Structured Feedback: Subspaces imposing sparsity or output constraints, with induced Riemannian geometry and embedded manifolds.
• Dynamic Output-Feedback (LQG): Parameterized by $(A_K, B_K, C_K)$, subject to GL$_n$ similarity orbits; the quotient space forms a Hausdorff manifold admitting global coordinate charts (e.g., Youla).
• Performance Measures: LQR offers smooth, gradient-dominated landscapes; $\mathcal{H}_\infty$ and LQG may be nonconvex/nonsmooth but retain regularity.
• Algorithmic Implications: Riemannian gradient descent, stability-retracting updates, and symmetry-exploiting optimization.

The following schematic classifies policy types:

Policy Class	Parameterization	Geometry	Objective	Landscape
Static State-Feedback	$K \in \mathbb{R}^{m\times n}$	Open, contractible	LQR, $\mathcal{H}_\infty$	Benign, regular
Structured Feedback	Subspace restriction	Submanifold	LQR, $\mathcal{H}_\infty$	Gradient-dominated
Dynamic Output-Feedback	$(A_K, B_K, C_K)$	Quotient manifold	LQG	Spurious saddles

5. Taxonomies in Reinforcement Learning for Robotics and Control

A comprehensive taxonomy of RL-based control policies for robotics is presented in (Ter et al., 11 Oct 2025), organized along algorithmic and application axes:

• MDP Formalism: $$(\mathcal{S}, \mathcal{A}, \mathcal{P}, \mathcal{R}, \gamma)$$ underpins all RL models, seeking $\pi^*$ maximizing expected discounted returns.
• Algorithmic Categories:
  • Value-Based: Q-Learning, DQN, Distributional RL
  • Policy-Based: REINFORCE, TRPO, PPO
  • Actor-Critic: A2C/A3C, DDPG, TD3, SAC

Category	Examples	Core Principle
Value-Based	Q-Learning, DQN, C51	Bellman updates, state-value learning
Policy-Based	REINFORCE, PPO, TRPO	Direct policy-gradient optimization
Actor-Critic	DDPG, TD3, SAC	Hybrid actor-value structure

Additional taxonomy dimensions include application domains (locomotion, manipulation, multi-agent, human-robot interaction), training pipelines (online, sim-to-real, offline, imitation), and deployment readiness levels (simulation to industrial deployment).

Key design patterns encompass actor-critic separation, replay buffers, entropy regularization, twin networks, hierarchical/meta learning, and maturity models guiding pipeline selection for deployment.

6. Unified Control Frameworks for Enterprise Governance and Compliance

Enterprise AI governance frameworks are characterized by a risk- and compliance-centric taxonomy. The Unified Control Framework (UCF) (Eisenberg et al., 7 Mar 2025) synthesizes a 15-type risk taxonomy (AI agency, fairness & bias, security, privacy, etc.), dovetails it with structured policy requirements, and enumerates a library of 42 controls. These controls map multi-domain risks to compliance mandates:

Control ID	Description	Primary Risk Domain(s)
001–005	Access, protection, validation ...	Security
012,013	Performance testing/monitoring	Performance & Robustness
014–016	Fairness testing, monitoring	Fairness & Bias
...	...	...

Mapping functions $$M_{R\rightarrow C}, M_{P\rightarrow C} \subseteq R\times C, P\times C$$ formalize many-to-many relationships between risks, policy requirements, and controls. Regulatory alignment (e.g., Colorado AI Act) is achieved via explicit coverage: each requirement is mapped to one or more controls. This enables policy designers to instantiate control portfolios that simultaneously mitigate risk and achieve compliance.

7. Generalization and Domain Transferability of Structured Taxonomies

Structured policy taxonomies—whether economic, security, optimal control, RL, or enterprise—share a meta-structure: hierarchical decomposition, parametrized atomic controls, coverage verification, and formal mappings between intent, realization, and deployment specifics. Theoretical constructs (incidence matrices, quotient manifolds, policy mappings) generalize across engineered domains, providing templates for completeness, interoperability, and rigorous evaluation.

A plausible implication is that further research can exploit these formal structures to develop universal taxonomy engines that automate policy enumeration, simulation interfacing, risk mapping, and real-world system deployment pipelines. The standardized, trait-based approach ensures no gap in control coverage, facilitating reliable model calibration, formal verification, and cross-domain policy transfer.