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

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

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

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

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

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

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

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