data-driven-distributed-control

name: data-driven-distributed-control description: > Data-driven distributed controller synthesis using spatial regret optimization. For synthesizing optimal distributed controllers directly from frequency-response data without requiring a parametric system model. Use when: (1) designing distributed control systems from experimental data, (2) comparing spatial regret vs H2/Hinf performance, (3) building data-driven controllers with communication structure constraints, (4) model-free controller synthesis for networked systems.

Data-Driven Distributed Control via Spatial Regret

Core Methodology (arXiv:2605.02506)

Synthesize optimal distributed controllers directly from frequency-response data using spatial regret — measures performance gap between a structured distributed controller and an oracle with enhanced communication topology.

Key Concepts

Spatial Regret

• Quantifies the cost of distributed communication constraints
• Compares structured controller performance against an oracle with richer communication
• Relaxes topology assumptions: oracle can use any enhanced structure
• Provides a principled trade-off between communication cost and control performance

Data-Driven Synthesis

• Uses experimentally obtained frequency-response data (no parametric model needed)
• Preserves stability and desired communication structure
• Iterative solution (not single convex program) due to relaxed oracle assumptions
• Outperforms classical H2/Hinf designs in numerical benchmarks

Workflow

Step 1: Collect Frequency-Response Data

Obtain G(jw) from experiments or identification at discrete frequencies.

Step 2: Define Communication Structure

Specify which subsystems can communicate via structural constraint matrix S (S[i,j]=1 means subsystem i can access subsystem j measurements).

Step 3: Solve Spatial Regret Problem (Iterative)

1. Initialize controller K with desired structure
2. Compute oracle K_oracle with relaxed constraints
3. Minimize regret: min_K [J(K) - J(K_oracle)]
4. Iterate until convergence

Step 4: Validate

• Check stability margins
• Compare H2/Hinf performance metrics
• Verify communication structure preservation

Comparison: Spatial Regret vs Classical Methods

Pitfalls

• Iterative solution may not converge for ill-conditioned systems
• Frequency data quality critically affects synthesis result
• Oracle definition must be carefully chosen (too relaxed = trivial regret)

Reference

arXiv:2605.02506 — Gupta, Martinelli, Ferrari-Trecate, Furieri, Karimi (2026)