2093

Analysis of contraction theory and its application in the stability and control of dynamical systems

دكتر تخصصي

رياضي كاربردي گرايش تحقيق در عمليات

مركز تحصيلات تكميلي دانشگاه پيام نور

1403

1403/07/10

دكتر بشير نادري

دكتر حسن زارع

Dynamic Systems, Stability, Chaos, Control, Sychronitional, Contraction theory.

Chaotic systems are complex models of behavior and dynamic phenomena that seemed to be completely random and lawless. The control of these systems leads to a set of methods in mathematics that are used to manage and regulate the system. Stability is the most important performance characteristic in the analysis and design of control systems, which usually discussion stability points from Lyapunov theory. Considering that it is difficult to find a controller using the Lyapunov method, in this Thesis we introduce the contraction method under the title of controller design or a method for stability. Then we discuss the relationship between the contraction method and the graphical algorithm. We study the behavior of the chaotic nonlinear memristor system, such as bifurcation, attractor and Lyapunov exponents, which are characteristics of chaos. Since chaotic systems are sensitive to the initial conditions, their synchronization and control are essential issues. Graphical algorithm is used to control and synchronization the chaotic memristor system. Also, we use synchronization results for secure communication. Then we are checking the sum-of-squares (SOS) matrix method and while investigating the behavior of a number of systems without equilibrium points, we control and synchronize these systems with the help of the graphical algorithm and the sum-of-squares method.

1403/08/20

ابراهيمي

76793