Energy-constrained optimal strictly stealthy attacks in LQG systems

Cyber-physical systems (CPSs) are increasingly vulnerable to sophisticated and malicious attacks, making their security a critical concern in modern control and estimation systems. This paper investigates the problem of optimal timing for strictly stealthy linear attacks under energy constraints, formulated within the Linear Quadratic Gaussian (LQG) control framework from an adversarial perspective. When the attacker's energy budget is limited, only a finite number of attacks can be executed within a fixed time horizon. Therefore, the attacker must strategically schedule these attacks to maximise system performance degradation while remaining completely stealthy. An energy-constrained attack model is formulated, and the optimal attack timing strategy that leads to the greatest degradation in system performance under both strict stealthiness and energy constraints is derived analytically. The theoretical findings are validated through numerical simulations, which demonstrate the effectiveness and practical relevance of the proposed attack scheduling strategy.