Cost of Update Delay Minimization for Covert Cyber-Physical Systems: Co-Design of Communications and Control

Secure data transmission and real-time state updates are critical yet challenging requirements for Cyber-Physical Systems (CPS) to maintain stability under adversarial conditions. While existing works have separately explored covert communications for security and Age of Information (AoI) optimization for timeliness, their interdependencies remain unaddressed, leading to suboptimal trade-offs between detection resistance, control performance, and resource efficiency. To bridge this gap, this paper proposes a novel co-design framework that jointly optimizes covert communication and AoI-aware control strategies. First, we rigorously derive a linear relationship between average AoI and control cost, termed the Cost of Update Delay (CoUD), which quantifies how outdated information exacerbates state fluctuations and increases stabilization efforts. Building on Kosta et al.’s Geo/Geo/1 queuing model, a closed-form expression for average AoI is further established as a function of sampling rate and packet delivery probability, explicitly linking communication parameters to control efficacy. Subsequently, this paper formulate a constrained optimization problem to minimize CoUD while guaranteeing covertness against eavesdroppers, leveraging Dinkelbach’s transformation and Lagrangian duality to decouple nonlinear constraints, derive optimal sampling rates, and transmission powers. Simulation results demonstrate that the proposed co-design framework achieves significant reductions in CoUD and superior freshness compared to baseline methods, while robustly maintaining covertness requirements. Notably, the proposed integration of sampling rate adaptation into the detection error rate model markedly enhances both AoI performance and resource efficiency, outperforming state-of-the-art disjoint designs. Therefore, this work provides a unified methodology to harmonize security, timeliness, and stability in resource-constrained CPS.