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Physics-Based Communication Compression via Lyapunov-Weighted Event-Triggered Control

Abbas Tariverdi

TL;DR

The paper tackles the high energy cost of communications in networked control by introducing a static directional event-triggered mechanism that leverages the Lyapunov gradient to create a state-dependent half-space trigger. This approach exploits stability geometry to permit larger errors along safe directions while tightening bounds along destabilizing ones, and it proves global asymptotic stability with exclusion of Zeno behavior. In Monte Carlo validation, it achieves 43.6% fewer transmissions than optimally tuned isotropic baselines and up to 2.1x better control performance than time-varying alternatives. Additionally, it presents a Lyapunov Safety Gate to certify learning-based controllers in real time and discusses practical deployment considerations such as energy budgets, verification, and safety certification.

Abstract

Event-Triggered Control (ETC) reduces communication overhead in networked systems by transmitting only when stability requires it. Conventional mechanisms use isotropic error thresholds ($\|e\| \le σ\|x\|$), treating all directions equally. This ignores stability geometry and triggers conservatively. We propose a static directional triggering mechanism that exploits this asymmetry. By weighting errors via the Lyapunov matrix $P$, we define an anisotropic half-space scaling with instantaneous energy margins: larger deviations tolerated along stable modes, strict bounds where instability threatens. We prove global asymptotic stability and exclusion of Zeno behavior. Monte Carlo simulations ($N=100$) show 43.6\% fewer events than optimally tuned isotropic methods while achieving $2.1\times$ better control performance than time-varying alternatives. The mechanism functions as a runtime safety gate for learning-based controllers operating under communication constraints.

Physics-Based Communication Compression via Lyapunov-Weighted Event-Triggered Control

TL;DR

The paper tackles the high energy cost of communications in networked control by introducing a static directional event-triggered mechanism that leverages the Lyapunov gradient to create a state-dependent half-space trigger. This approach exploits stability geometry to permit larger errors along safe directions while tightening bounds along destabilizing ones, and it proves global asymptotic stability with exclusion of Zeno behavior. In Monte Carlo validation, it achieves 43.6% fewer transmissions than optimally tuned isotropic baselines and up to 2.1x better control performance than time-varying alternatives. Additionally, it presents a Lyapunov Safety Gate to certify learning-based controllers in real time and discusses practical deployment considerations such as energy budgets, verification, and safety certification.

Abstract

Event-Triggered Control (ETC) reduces communication overhead in networked systems by transmitting only when stability requires it. Conventional mechanisms use isotropic error thresholds (), treating all directions equally. This ignores stability geometry and triggers conservatively. We propose a static directional triggering mechanism that exploits this asymmetry. By weighting errors via the Lyapunov matrix , we define an anisotropic half-space scaling with instantaneous energy margins: larger deviations tolerated along stable modes, strict bounds where instability threatens. We prove global asymptotic stability and exclusion of Zeno behavior. Monte Carlo simulations () show 43.6\% fewer events than optimally tuned isotropic methods while achieving better control performance than time-varying alternatives. The mechanism functions as a runtime safety gate for learning-based controllers operating under communication constraints.

Paper Structure

This paper contains 16 sections, 4 theorems, 17 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Main Results
  4. Directional Triggering Condition
  5. Stability Analysis
  6. Exclusion of Zeno Behavior
  7. Numerical Validation
  8. System Setup
  9. Results and Discussion
  10. Technological Impact
  11. Energy Budget Analysis
  12. Time-Independent Verification
  13. Safety Certification for Learning-Based Controllers
  14. Conclusion
  15. Applicability and Limitations
  16. ...and 1 more sections

Key Result

Proposition 1

The set $\mathcal{T}_{\mathrm{dir}}$ defines a half-space in error coordinates, bounded by the hyperplane orthogonal to $v = (PBK)^\top x$.

Figures (8)

  • Figure 1: Triggering constraints in error space $(e_1, e_2)$. (a) Isotropic constraint: permissible errors form a sphere of radius $\sigma\|x\|$. (b) Directional constraint: permissible errors form a half-space bounded by a hyperplane orthogonal to $\nabla V = 2Px$ (orange arrow). Errors aligned with $\nabla V$ trigger events; orthogonal errors do not.
  • Figure 2: Stability margin analysis. The curve shows the decay rate $\lambda_{\min}(Q) - \sigma\lambda_{\max}(P)$ versus $\sigma$. The vertical dashed line marks the bound $\sigma_{\max} = 0.5528$ from Theorem \ref{['thm:stability']}. The operating point $\sigma = 0.10$ maintains a large margin below the limit.
  • Figure 3: State trajectories for $x_0 = [4, 3]^\top$. (a) State magnitude $\|x(t)\|$. (b) Phase portrait. Mazo (red) oscillates more than Proposed (blue) or Tabuada (teal) due to its loose temporal envelope.
  • Figure 4: Event timing for $x_0 = [4, 3]^\top$ (first 10 s). Totals: Proposed 82, Mazo 86, Tabuada 156.
  • Figure 5: Lyapunov function decay (log scale). Proposed and Tabuada decay monotonically. Mazo allows non-monotonic behavior.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Definition 1: Triggering Sets
  • Proposition 1: Half-Space Structure
  • proof
  • Theorem 1: Asymptotic Stability
  • proof
  • Theorem 2: Positive MIET
  • proof
  • Theorem 3: Lyapunov Safety Gate
  • proof
  • Remark 1