Synchronization of N-Non-Linear Slave Systems with Master System Using Non-Adaptive and Adaptive Coupled Observers

Synchronization of N-slave chaotic systems with a master system is a challenging task, particularly in recent times. In this paper, a novel methodology is proposed for synchronizing the N number of slave systems with a master system. The proposed methodology is based on coupled adaptive synchronous observers. The difference between the corresponding states of master and slave systems is converged to the origin by means of a novel feedback control scheme to achieve synchronization between the master and slave systems. The efficacy of the proposed methodology is verified through a simulation of FitzHugh–Nagumo non-linear systems in MATLAB. The simulation results validate and prove claims, and these systems are successfully synchronized by CCS and CCAS observer-based control

Distributed H ∞ state estimation for stochastic delayed 2-D systems with randomly varying nonlinearities over saturated sensor networks

In this paper, the distributed H ∞ state estimation problem is investigated for the two-dimensional (2-D) time-delay systems. The target plant is characterized by the generalized Fornasini-Marchesini 2-D equations where both stochastic disturbances and randomly varying nonlinearities (RVNs) are considered. The sensor measurement outputs are subject to saturation restrictions due to the physical limitations of the sensors. Based on the available measurement outputs from each individual sensor and its neighboring sensors, the main purpose of this paper is to design distributed state estimators such that not only the states of the target plant are estimated but also the prescribed H ∞ disturbance attenuation performance is guaranteed. By defining an energy-like function and utilizing the stochastic analysis as well as the inequality techniques, sufficient conditions are established under which the augmented estimation error system is globally asymptotically stable in the mean square and the prescribed H ∞ performance index is satisfied. Furthermore, the explicit expressions of the individual estimators are also derived. Finally, numerical example is exploited to demonstrate the effectiveness of the results obtained in this paper

Convolutional Neural Networks as 2-D systems

This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of linear filters, is realized in state space as a linear time-invariant 2-D system. The overall convolutional Neural Network composed of convolutional layers and nonlinear activation functions is then viewed as a 2-D version of a Lur'e system, i.e., a linear dynamical system interconnected with static nonlinear components. One benefit of this 2-D Lur'e system perspective on CNNs is that we can use robust control theory much more efficiently for Lipschitz constant estimation than previously possible

Two-dimensional dissipative control and filtering for Roesser model

This paper investigates the problems of two-dimensional (2-D) dissipative control and filtering for a linear discrete-time Roesser model. First, a novel sufficient condition is proposed such that the discrete-time Roesser system is asymptotically stable and 2-D (Q, S,R)-α-dissipative. Special cases, such as 2-D passivity performance and 2-D H∞ performance, and feedback interconnected systems are also discussed. Based on this condition, new 2-D (Q, S,R)-α-dissipative state-feedback and output-feedback control problems are defined and solved for a discrete-time Roesser model. The design problems of 2-D (Q, S,R)-α-dissipative filters of observer form and general form are also considered using a linear matrix inequality (LMI) approach. Two examples are given to illustrate the effectiveness and potential of the proposed design techniques.Choon Ki Ahn, Peng Shi, and Michael V. Basi