Convex Opt. for EH-DoS-Resilient State Estimation (47 chars)

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Convex Optimization for Remote State Estimation under Energy-Harvesting-Aware Denial-of-Service Attacks — 8-slide presentation with rich mathematical and conceptual content. Include automatically generated diagrams and flowcharts. Cover background, system model, problem definition, convex optimization formulation (LMI-based SDP), numerical results (scalar and 2x2 examples), and conclusions. Maintain technical depth and clarity, suitable for a 3-minute research presentation.

8-slide talk on convex optimization (LMI-SDP) for remote state estimation in CPS with energy-harvesting sensors under DoS attacks. Minimizes error covariance via joint sensor policy and estimator gain

December 6, 20258 slides
Slide 1 of 8

Slide 1 - Convex Optimization for Remote State Estimation under Energy-Harvesting-Aware DoS Attacks

This title slide features the research topic "Convex Optimization for Remote State Estimation under Energy-Harvesting-Aware DoS Attacks." The subtitle credits the presenter [Your Name] and notes it as a 3-Minute Research Overview.

Convex Optimization for Remote State Estimation under Energy-Harvesting-Aware DoS Attacks

Presenter: [Your Name] | 3-Minute Research Overview

Speaker Notes
Presenter: [Your Name]. 3-minute research overview.
Slide 1 - Convex Optimization for Remote State Estimation under Energy-Harvesting-Aware DoS Attacks
Slide 2 of 8

Slide 2 - Background

This slide outlines remote state estimation in cyber-physical systems using energy-harvesting sensors that transmit packets to a remote estimator. It highlights DoS attacks that jam transmissions by exploiting energy profiles, with the goal of minimizing error covariance under attacks.

Background

  • Remote state estimation in CPS with energy-harvesting sensors
  • Sensors transmit packets to remote estimator
  • DoS attacks jam transmissions, aware of energy profiles
  • Goal: Minimize error covariance under attacks
Slide 2 - Background
Slide 3 of 8

Slide 3 - System Model

The slide illustrates a system model featuring an energy-harvesting sensor that generates states \(xk\) and measurements \(yk\), transmitted over a wireless channel under DoS jammer attack to a remote estimator for state reconstruction. The sensor's energy queue \(Ek\) evolves based on harvested energy \(Hk\) and transmission costs.

System Model

!Image

  • Energy-harvesting sensor generates states xk, measurements yk.
  • Wireless channel attacked by DoS jammer.
  • Remote estimator reconstructs states from received data.
  • Energy queue Ek evolves with harvest H_k and tx cost.

Source: Photo by Compare Fibre on Unsplash

Slide 3 - System Model
Slide 4 of 8

Slide 4 - Problem Definition

The slide defines the problem of minimizing the trace of the error covariance matrix \(Pk\). It involves jointly optimizing the sensor policy \(\pi\) and estimator gain \(K\) under an EH-aware DoS attack budget \(\Gamma\), while handling stochastic Denial-of-Service attacks.

Problem Definition

  • Minimize trace of error covariance matrix Pk
  • Jointly optimize sensor policy π and estimator gain K
  • Under EH-aware DoS attack budget Γ
  • Handle stochastic Denial-of-Service attacks

Source: Convex Optimization for Remote State Estimation under Energy-Harvesting-Aware Denial-of-Service Attacks

Slide 4 - Problem Definition
Slide 5 of 8

Slide 5 - Convex Optimization Formulation

The slide presents a convex optimization formulation with an SDP on the left that minimizes trace(P) subject to P ≽ A(P - E)Aᵀ + γQ and LMIs ensuring closed-loop stability via Lyapunov inequalities. On the right, it specifies energy constraints as Pr(Ek ≥ c) ≥ 1 - ε to model probabilistic energy availability in energy-harvesting sensors under DoS attacks.

Convex Optimization Formulation

SDP FormulationEnergy Constraints
Minimize trace(P) s.t. P ≽ A(P - E)Aᵀ + γQ, and LMIs ensuring closed-loop stability (Lyapunov inequalities).Pr(Ek ≥ c) ≥ 1 - ε, capturing probabilistic energy availability in energy-harvesting sensors under DoS attacks.
Speaker Notes
Highlight the SDP minimizing estimation error covariance trace(P), with Lyapunov LMIs for stability and probabilistic energy constraints under DoS.
Slide 5 - Convex Optimization Formulation
Slide 6 of 8

Slide 6 - LMI-based SDP

This slide outlines an LMI-based SDP method that formulates LMIs for Riccati-like inequalities and solves them using the CVX solver. It produces optimal outputs π and K, supporting both scalar and multi-dimensional cases.

LMI-based SDP

!Image

  • Formulate LMIs for Riccati-like inequalities
  • Solve SDP using CVX solver
  • Outputs: optimal π and K
  • Handles scalar/multi-dimensional cases

Source: Wikipedia

Speaker Notes
Flowchart: Formulate LMIs for Riccati-like inequalities. Solve SDP via CVX. Outputs: Optimal tx probs π*, gain K*. Handles scalar/multi-dim.
Slide 6 - LMI-based SDP
Slide 7 of 8

Slide 7 - Numerical Results: Scalar Case

The scalar case numerical results show a 25% MSE reduction for the attack-aware method versus the baseline. Under a DoS attack with intensity Γ=0.3, the energy queue remains stable with faster covariance convergence.

Numerical Results: Scalar Case

  • 25%: MSE Reduction
  • Attack-aware vs baseline

  • 0.3: Attack Intensity Γ
  • DoS attack parameter

  • Stable: Energy Queue
  • Long-term bounded behavior

  • Faster: Covariance Convergence
  • Error vs time plot

Slide 7 - Numerical Results: Scalar Case
Slide 8 of 8

Slide 8 - Conclusions

The conclusions highlight that EH-aware DoS significantly impacts estimation, while convex SDP delivers robust policies. Future work targets multi-sensor networks, with the key insight that proactive transmission scheduling outperforms reactive methods—thank you for your attention!

Conclusions

• EH-aware DoS significantly impacts estimation

  • Convex SDP yields robust policies
  • Future: Multi-sensor networks
  • Key insight: Proactive tx scheduling beats reactive

Thank you for your attention!

Source: Convex Optimization for Remote State Estimation under Energy-Harvesting-Aware Denial-of-Service Attacks

Speaker Notes
Highlight impacts, SDP benefits, future work, and key insight. Closing: 'Proactive scheduling beats reactive.' (4 words). CTA: 'Explore multi-sensor networks together.' (4 words).
Slide 8 - Conclusions

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