stability-goal-obfuscation

name

stability-goal-obfuscation

description

Stability-goal obfuscation tradeoff methodology for autonomous agents. Addresses the problem that Lyapunov-stable goal-directed trajectories are inherently legible to Bayesian observers, leaking intent. Combines control Lyapunov functions (CLFs), probabilistic control barrier functions (PCBFs), and Rao-Blackwellized particle filter (RBPF) belief-state analysis to maintain task stability while obfuscating intent from passive observers. Use when: designing privacy-preserving autonomous systems, adversarial trajectory planning, intent privacy, safety-critical control, control barrier functions, Lyapunov stability with privacy constraints.

Stability-Goal Obfuscation Tradeoff

Framework for maintaining task stability while preventing intent inference by adversarial observers, based on Wang, Guralnik & Dixon (arXiv:2605.06630, May 2026).

Problem

Goal-directed agents under Lyapunov-based control are intrinsically legible: the contractive dynamics of a Lyapunov basin of attraction concentrates a Bayesian observer's posterior belief over the agent's latent intent parameters (goal location, radius, arrival time). Task-optimal trajectories are the most information-leaking.

Core Methodology

1. Dual-State Control Problem

Joint control on:

• Physical state x: agent dynamics ẋ ∈ u + d̄B (fully actuated, bounded disturbance)
• Belief state b: observer's RBPF belief over possible agent goals

The controller must satisfy both a tracking constraint (CLF) and a privacy constraint (PCBF) simultaneously.

2. KL-Based Information Leakage Measurement

• Observer uses Rao-Blackwellized particle filter (RBPF) with N particles over discrete goal samples
• Information leakage measured as KL divergence between prior and posterior over goals
• Online-computable at each RBPF update step
• Privacy requires maintaining leakage below a threshold with high probability

3. Probabilistic Control Barrier Functions (PCBFs)

Key innovation: derive separate PCBF conditions for:

• Bayesian update step: posterior concentration from new observations
• Resampling step: particle weight redistribution

Combined PCBF guarantees privacy across the full RBPF update cycle.

4. Joint Feasibility Analysis

The tracking envelope (physical feasibility) and privacy constraint (belief-state feasibility) interact:

• Tight privacy bounds shrink feasible control set
• Loose bounds may fail to obfuscate
• Feasibility depends on disturbance bounds d̄, RBPF particle count N, and measurement noise

Implementation Pattern

# QP formulation (per timestep):
# min  ||u - u_nom||²
# s.t.  ∂V/∂x · f(x,u) ≤ -α(V(x))          # CLF (stability)
#       P[PCBF(b, u) ≥ 0] ≥ 1 - ε          # PCBF (privacy, probabilistic)
#       u ∈ U                                # input constraints

Where:

• u_nom: nominal task-optimal control
• V: control Lyapunov function
• PCBF: probabilistic barrier function on belief state
• ε: acceptable privacy violation probability

When to Apply

• Autonomous vehicles operating in adversarial environments
• Military/aerospace systems requiring intent privacy
• Multi-agent systems where intent leakage compromises coordination
• Any Lyapunov-stable controller operating under observation

Key References

• arXiv:2605.06630 — Wang, Guralnik, Dixon (2026)
• Ames et al. (2016, 2019) — Control Barrier Functions
• Dragan et al. (2013) — Legible robot motion planning
• Wang et al. (2025b) — Intent inference via RBPF

Pitfalls

• RBPF requires sufficient particle count for accurate belief estimation
• Privacy constraint may be infeasible if disturbance bounds are too tight
• Joint feasibility analysis is problem-specific; no universal bounds
• PCBF derivation requires careful treatment of both update and resampling steps