Executive Summary : | Today nonlinear dynamical systems are used to describe a model for a great variety of scientific phenomena ranging from social life and physical science to engineering and technology. To apply to real-time models suitable adaptive controller should be designed for stability analysis by using a novel framework of quantum neural networks (QNNs) with several optimization algorithms. As an application part, theoretical findings could be used for secure communications and image processing. The proposed model parameters should be estimated to apply the adaptive rules by constructing suitable Lyapunov-based methods. In recent years, while modeling a system with delays, impulses and uncertainties such as external noise/disturbance are unavoidable. The suitable Lyapunov Krasovskii theorem will be used to study the stability criteria. To find the control parameters, the QNNs will be used, and several optimization algorithms are correspondingly used to optimize the cost function. In the application aspect, developed algorithms will use for secure communication and image filters via QNNs chaotic controllers. The parameters of adaptive controllers will be obtained by using the QNNs scheme and solving the Lyapunov functions. Numerical simulations will be undertaken by using the LMI toolbox and neural network control toolbox in MATLAB. Chaos synchronization using adaptive QNNs and its application could be entrusted for secure communication. Taylor series expansion will be used to obtain a linear relation between the output of QNN and its adaptive parameters. The significant contribution of this study is the application of adaptive control theory and the Lyapunov type stability technique to develop a controller for a dynamic model of physical systems in the presence of uncertainties. The QNN is used to estimate uncertainties in the receiver and improve the accuracy of synchronization for recovering the message signal in cryptography. The creation of complex cryptographic systems based on QNNs will be used to develop the secure computers, so as to guarantee internet security for all users. In this way, the obtained chaotic synchronization using adaptive QNNs will be used to design better security to forthcoming generations for new industrial supporting systems. |