Application Of Finite Time Control In Two Types Of Chaotic Systems

Chaos control,as an extremely important part of non-linear scientific research,has a wide range of applications in engineering,physics,and biology.The fractional-order hyperchaotic financial model and the integer-order chaotic financial model have a very significant role in analyzing the financial crisis.The state variables represent the interest rate,investment demand,and price index to describe the dynamics of the model.And use the strong robustness and convergence of finite time control to effectively eliminate chaos and ensure normal operation under external interferenceThe first chapter: Introducing the research status of chaos control in foreign countries and the development process of chaos.The second chapter: Outlines the definition,characteristics and identification of chaos.The stability of integer-order system and fractional-order system are described and proved respectively,and the chaotic attractor graph,maximum Lyapunov exponent graph,time history graph,etc.of the system are described by examples using Matlab numerical simulation methods.The third chapter: To introduce the theorem of fractional-order finite-time stability is discussed.The fractional-order hyperchaotic financial model is briefly described and its dynamics are demonstrated through numerical simulation.The controller is designed based on the fractional-order finite-time stability theorem,and its correctness and feasibility are verified through theory and Matlab numerical simulation.Because in the process of chaos control,there is no possibility of external interference,so the external interference term is added to perform numerical simulation again.The final control chart can prove that the external interference also reaches stability within a limited time.Chapter 4: The integer-order finite-time stability theorem and its lemma are explained.The maximum Lyapunov exponential graph,chaotic attractor graph,and time series graph are used to describe the dynamics of integer-order financial systems.A time-stable controller was designed to fit the system,and then the effectiveness and correctness of the control scheme were verified by using fractional-order stability theory and numerical simulation.Chapter 5: Summary of the full text work and prospects for future chaos control.