Optimal fusion state estimator for a multi-sensor system subject to multiple packet dropouts

The safety region-based model predictive control for discrete-time systems under deception attacks

“…is the monotonically decreasing function | to be ≥ designed off-line such that (4) has the favorable control performance. Correspondingly, the constraint (7), which is used as a detection condition, is used to replace the original input constraint (2). R(u ˆk+s k ) and U ˜k+s k are functions which would be given in Theorem 1 and…”

“…| 2 where we | have proved that (6) is the sufficient condition of (7). That is, we can use (7) as the so-called safety region of the CA detector such that the CA detector has the ability to detect the received input signals.…”

“…Remark 2. In Theorem 1 and Theorem 2, we give the process of designing the the safety-region-based constraint R(û k+s|k ) ∈ Ũk+s|k in (7). In reality, the single-input system is a special case of the multi-input system such that Theorem 2 is a more general conclusion on designing the constraint R(û k+s|k ) ∈ Ũk+s|k .…”

“…There are some differences in the form of (7) between two cases. Furthermore, (7) is tighter than (2) while the solution of Problem 1 does not change, that is, the solution obtained under constraints (2), ( 5) and ( 6) is the same as that under (5), ( 6) and (7). The details are shown in the following Theorems 1-2. k from the sequence stored in the buffer and applies it to the actuator.…”

“…The control system oriented cyber-attacks can be categorized as the Denial-of-Service (DoS) attack which blocks data transmission [7][8][9][10][11][12][13] and the deception attack which impacts the integrity of data [14]. Compared with the DoS attack, the deception attack is more stealthy which could compromise the controlled system without triggering any alarms.…”