stability-goal-obfuscation

# 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 ```python # 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