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In this paper, the fault estimation problem is studied for a class of nonlinear networked control systems with imperfect measurements. A novel measurement model is proposed to take time-varying delays, random packet dropouts, and the packetdropout compensation into consideration simultaneously. After properly augmenting the states of the original system and the fault estimation filter, the addressed fault estimation problem is converted into an auxiliary H• filtering problem for a stochastic parameter system. In terms of matrix inequalities, a sufficient condition for the existence of the fault estimation filter is derived that depends on the packet dropout rate, the upper and lower bounds of time delays, and the size of the consecutive packet dropouts. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.Theorem 2. For a given scalar g > 0, the filtering error system (12) is stochastically stable and the H• performance constraint (13) is satisfied for all nonzero w(k), if there exist symmetric matrices P1 > 0, P3 > 0, Q1 > 0, Q2 > 0, and Q3 > 0;

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Merging behavior is inevitable at on-ramp bottlenecks and is a significant factor in triggering traffic breakdown. In modeling merging behaviors, the gap acceptance theory is generally used. Gap acceptance theory holds that when a gap is larger than the critical gap, the vehicle will merge into the mainline. In this study, however, analyses not only focus on the accepted gaps, but also take the rejected gaps into account, and the impact on merging behavior with multi-rejected (more than once rejecting behavior) gaps was investigated; it shows that the multi-rejected gaps have a great influence on the estimation of critical gap and merging prediction. Two empirical trajectory data sets were collected and analyzed: one at Yan'an Expressway in Shanghai, China, and the other at Highway 101 in Los Angeles, USA. The study made three main contributions. First, it gives the quantitative measurement of the rejected gap which is also a detailed description of non-merging event and investigated the characteristics of the multi-rejected gaps; second, taking the multi-rejected gaps into consideration, it further expanded the concept of the "critical gap" which can be a statistic one and the distribution function of merging probability with respect to such gaps was analyzed by means of survival analysis. This way could make the full use of multi-rejected gaps and accepted gaps and reduce the sample bias, thus estimating the critical gap accurately; finally, considering multi-rejected gaps, it created logistic regression models to predict merging behavior. These models were tested using field data, and satisfactory performances were obtained.

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This article investigates the fault detection problem in finite-frequency domain for a class of nonlinear networked systems under stochastic cyber-attacks.A novel adaptive event-triggered scheme is introduced to mitigate the transmission burden of the network. A unified measurement model is proposed to take the randomly occurring cyber-attacks and the transmission delays into account simultaneously. Under the consideration of fault sensitivity and disturbance robustness, the addressed fault detection problem is converted into an auxiliary H − ∕H ∞ filtering problem by properly augmenting the states of the original system and the fault detection filter. Intensive stochastic analysis is carried out to obtain sufficient conditions for the existence of the desired fault detection filter, and the corresponding optimal filter parameters can be easily derived by solving a convex optimization problem. Finally, an illustrative example is presented to show the effectiveness and applicability of the proposed method.

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