Extremum Seeking Under Persistent Gradient Deception: A Switching Systems Approach

Online Optimization of LTI Systems Under Persistent Attacks: Stability, Tracking, and Robustness

“…Moreover, by condition (13), the defense mechanism prevents the emergence of Zeno behavior in the system, permitting only switches of σ that satisfy an average dwell-time constraint. Similar attack models have been considered in the literature; see [13,20,11]. Indeed, conditions ( 12)-( 13) are quite general: they capture periodic or aperiodic attacks, and they allow a finite number of consecutive switches in every interval of time of sufficiently large length.…”

“…On the other hand, gradient-flow controllers have been used to drive the equilibrium point of the traffic flows on the highway system towards the solution of a network-level problem as explained in, e.g., [30] and [36]. It then follows that the attack models consider in (11) can be used to capture adversarial jamming of the feedback gains of the ALINEA controller, or attacks acting on the control directions obtained from the gradient flow algorithm.…”

“…The model (11) is also applicable to several applications in robotics, such as the control of autonomous vehicles using navigation laws based on potential and anti-potential functions; see [37,38,39]. Indeed, in this scenario, it is common to approximate the vehicle dynamics as a linear system (3) for which an internal feedback loop is designed to stabilize an external reference u; see [40].…”

“…In general, the internal controller is designed to guarantee a unitary DC gain, and to operate in a faster time scale (limited by the actuator dynamics of the vehicle), such that the "steady state" of the vehicle satisfies x * = u, where x can model positions or velocities. The input u is then regulated via a gradient flow of the form (11) aiming to converge to the minimizer (e.g., the target point) of an artificial potential field. In this case, to prevent the vehicle from converging to the target, an external attacker can persistently alter the sign of the gradient dynamics, i.e., M σu ∈ {I, −I}, effectively moving the vehicle away from the target.…”

“…Recently, [7] established exponential stability results for the interconnection of a switched LTI system and a hybrid feedback controller based on accelerated gradient dynamics with resets. Finally, [11] studied extremumseeking algorithms for static optimization problems under deception attacks.…”