Robust model predictive control for networked control systems with quantisation

Transmission Reliability Evaluation for Wireless Sensor Networks

“…At time in mesh WSNs, ,sink ( , ) is the probability that in the disjoint minimal path sets (from the source node to sink) there exists at least one path whose packet delivery rate is greater than the threshold ( , ) of th transmission, as shown in (11). Mesh ( , ) is the probability that Path( ,sink) ( , ) is greater than the uplink transmission threshold ( , ) in mesh WSNs, as shown in (12), where Path( ,sink) ( , ) represents the reliability of the th path from the source node to sink:…”

Moving Horizon Estimation for Networked Systems With Quantized Measurements and Packet Dropouts

“…is a quantizer and is assumed to be of the logarithmic type [37], [38]. The set of quantized levels is described by (3) where the parameter is the quantization density, and the logarithmic quantizer is defined as (4) where , , .…”

“…Moreover, if matrix is selected such that (37) Then, the sequence converges exponentially to the steady value . Proof: Define (38) Then, by the definition of , the estimation error is given by (39) Using (14), one obtains (40) Moreover, by applying the operator to the error dynamics and using triangular inequalities, one has (41)…”

“…Remark 5: It can be seen from Theorem 2 that the sequence of the estimation error is decay-rate-dependent, where the exponential decay rate depends on the quantization density and packet dropout status with given parameter . Thus, condition (37) implicitly establishes a relation between quantization density , packet received probability and the upper bound of . Remark 6: In Theorem 2, we have provided the stability properties of the optimal estimator (32).…”

“…In a similar way, we can also obtain the stability properties of the approximate estimator (33) by replacing the scalar parameter with a fixed value . Corollary 1: Given a pair , a quantization density and a packet received probability , if Assumptions 1-3 hold, then the norm of the estimation error for the approximate estimator (33) In order to ensure the convergence of the upper bound of the state estimation error sequence, the following proposition is given to guarantee condition (37).…”