Cyber-attack detection via non-linear prediction of IP addresses: an innovative big data analytics approach

Computer network systems are often subject to several types of attacks. For example, an excessive traffic load sent to a web server for making it unusable is the main technique introduced by the Distributed Denial of Service (DDoS) attack. A well-known method for detecting attacks consists in analyzing the sequence of source IP addresses for detecting possible anomalies. With the aim of predicting the next IP address, the Probability Density Function of the IP address sequence is estimated. Anomalous requests are detected via predicting source’s IP addresses in future accesses to the server. Thus, when an access to the server occurs, the server accepts only the requests from the predicted IP addresses and it blocks all the others. The approaches used to estimate the Probability Density Function of IP addresses range from the sequence of IP addresses seen previously and stored in a database to address clustering, for instance via the K-Means algorithm. Instead, the sequence of IP addresses is considered as a numerical sequence in this paper, and non-linear analysis of this numerical sequence is applied. In particular, we exploited non-linear analysis based on Volterra Kernels and Hammerstein models. The experiments carried out with datasets of source IP address sequences show that the prediction errors obtained with Hammerstein models are smaller than those obtained both with the Volterra Kernels and with the sequence clustering based on the K-Means algorithm.

Nonfragile H ∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models

This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust H ∞ disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse nonlinear functions of polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, H ∞ criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness.

A Unified Approach for the Identification of Wiener, Hammerstein, and Wiener–Hammerstein Models by Using WH-EA and Multistep Signals

Wiener, Hammerstein, and Wiener–Hammerstein structures are useful for modelling dynamic systems that exhibit a static type nonlinearity. Many methods to identify these systems can be found in the literature; however, choosing a method requires prior knowledge about the location of the static nonlinearity. In addition, existing methods are rigid and exclusive for a single structure. This paper presents a unified approach for the identification of Wiener, Hammerstein, and Wiener–Hammerstein models. This approach is based on the use of multistep excitation signals and WH-EA (an evolutionary algorithm for Wiener–Hammerstein system identification). The use of multistep signals will take advantage of certain properties of the algorithm, allowing it to be used as it is to identify the three types of structures without the need for the user to know a priori the process structure. In addition, since not all processes can be excited with Gaussian signals, the best linear approximation (BLA) will not be required. Performance of the proposed method is analysed using three numerical simulation examples and a real thermal process. Results show that the proposed approach is useful for identifying Wiener, Hammerstein, and Wiener–Hammerstein models, without requiring prior information on the type of structure to be identified.