Resilient control under Denial-of-Service: Robust design

Abstract

Abstract-In this paper, we study networked control systems in the presence of Denial-of-Service (DoS) attacks, namely attacks that prevent transmissions over the communication network. The control objective is to maximize frequency and duration of the DoS attacks under which closed-loop stability is not destroyed. Analog and digital predictor-based controllers with state resetting are proposed, which achieve the considered control objective for a general class of DoS signals. An example is given to illustrate the proposed solution approach.

Resilient filtering for cyber‐physical systems under denial‐of‐service attacks

“…Thus, combining (19) with (23), we can derive ΔV( (k), (k)) < V( (k), (k)), which can be reformulated as follows:…”

“…Vivid examples with reference to this process involving the active and silent subintervals of DoS attacks were properly depicted in ( Figure 2 in the work of De Persis and Tesi 7 and Figure 2 in the work of Wu et al 25 ). In that case, for the time interval [1,19), we can see n (1,19) = 3 while the number of total switchings is 5, which in turn verifies that the number of DoS attacks is not equal to the total switching times obviously. Thus, obviously, for considered time interval [0, k[, the number of total switchings  (0, k) = n(0, k) +n ≤ 2n(0, k), wheren represents the switching times from mode 0 to mode 1, and obviously, for the prescribed time domain [0, k), we havē n ≤ n(0, k).…”

“…Remark Original discussions concerning with frequency and duration of DoS attacks are stemmed from the works of De Persis and Tesi and Feng and Tesi . The drastic difference is that, compared with the voice for continuous‐time physical layer, our assumptions and can be seen as a counterpart of discrete‐time type.…”

“…Thus, this model plays an important role to investigate resilient control issues. Feng and Tesi focused on designing maximal DoS parameters while ensuring close‐loop stability and researched resilient control problems toward distributed systems as well as data‐rates limitation systems, respectively. Besides, Wakaiwi et al researched quantized stabilization issues .…”

Robust event‐triggered model predictive control for cyber‐physical systems under denial‐of‐service attacks

“…Here, a general DoS model is considered, which the attack behavior is characterized as time by posing restrictions on the frequency and duration merely. Denote by with h 0 ≥ 0 the sequence of DoS off/on transitions, which are the time instants when DoS attacks transform from null (transmission attempts are all successful) to one (transmission attempts fail) . The n th DoS interval is defined as H n ={ h n }∪[ h n , h n + τ n ), where is its length.…”