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Study On Chaos Anti-control And Its Application Of Continuous-time And Switching Systems

Posted on:2017-01-29Degree:DoctorType:Dissertation
Country:ChinaCandidate:C Y HanFull Text:PDF
GTID:1108330485478446Subject:Control Science and Engineering
Abstract/Summary:PDF Full Text Request
Generally speaking, the basic problem of chaos anti-control (chaotic) is divided into two categories:chaos anti-control of discrete-time system, chaos anti-control of continuous-time system and switching system. Although the basic principle of the anti-control can be as the starting point of research in these two types of problems, there are large differences in the way and progress of study. Since the concept of chaos anti-control was first put forward in 1994, substantial progress has been made in the study of discrete-time system for chaos anti-control. It can follow a very strict theories and methods to solve them. Though a certain progress has been made in the study of chaos anti-control for continuous-time system, the effective solutions in theory has not been find. Most of methods are still the parameters of the numerical level "try".In view of this, this dissertation is devoted to find the origins of these differences between the chaos anti-control of continuous-time system and the chaos anti-control of discrete-time system, looking for the chaos anti-control methods of continuous-time system and switching system, and exploring the problem of chaos anti-control from the theory and application. In addition, the classic Logistic map was improved and its application on the image encryption was further studied in this dissertation.The main research works of this dissertation are as follows.1. Based on the heteroclinic Shil’nikov theorem, a chaos anti-control method of linear switching system is proposed. Firstly, two fundamental linear systems are constructed. Then, a two-piecewise linear chaotic system which satisfies the heteroclinic Shil’nikov theorem is generated by constructing heteroclinic loop between equilibrium points of the two fundamental systems via switching controller. Finally, another multi-piecewise linear chaotic system which also satisfies the heteroclinic Shil’nikov theorem is obtained via alternate translation of the two fundamental linear systems and heteroclinic loop construction of adjacent equilibria for the multi-piecewise linear system. According to the proposed method, two typical chaotic systems are given to demonstrate the effectiveness and general of the method. The results of analog circuit experiment further verify the effectiveness of the proposed method.2. A novel chaos anti-control method is developed for a nonlinear switching system. This approach takes an unstable nonlinear system as the fundamental system. A multi-piecewise nonlinear system is constructed via linear translation of the fundamental system. Then, a chaotic system which satisfies the Shil’nikov theorem is generated by constructing heteroclinic loop between adjacent equilibria for the multi-piecewise nonlinear system by switching control. At the same time, based on the theory of topological horseshoe, the existence of chaos is proved theoretically. In addition, a circuit is designed and implemented for the chaotic system. The circuit implementation shows the effectiveness of the proposed systematic methodology. Due to the linear system is a special form of the nonlinear system, this method has more universality and generality compared with the existing chaotification based on linear systems switching control, and it is not only suitable for nonlinear system but also for linear systems.3. Taking the global boundness of the orbit, dissipation, also equipped with positive, negative and zero Lyapunov exponent as the breakthrough point of the research, a hyperchaos anti-control method of continuous-time linear system is proposed. By using this method, just a nonlinear function can easily realize the hyperchaotification of a controlled continuous-time linear system and the maximum of the number of the positive Lyapunov exponent for a certain dimension system. According to the proposed hyperchaos anti-control method, several hyperchaotic systems are given as an instance which proved that the method is feasible and generality.4. A new three dimensional non-autonomous system is constructed by the introduction of a sine excitation signal to a three-dimensional autonomous Lorenz system. Through appropriately adjusting the frequency of the sine function, the system can produce hyperchaotic attractor, chaotic attractor and high periodic orbits. Basic dynamic characteristics of the system are analyzed, such as the characteristics of the equilibrium point, Lyapunov dimension, Lyapunov exponent and bifurcation diagram changed with the frequency or the amplitude of the sine function, etc. In addition, a analog circuit and a digital circuit are designed and implemented respectively. The experimental results verify the effectiveness of the proposed method.5. Scale transformation and complex mapping are used to improve the Logistic map respectively. Scale transformation for the Logistic map can arbitrarily expend its mapping region and chaotic range, can improve the randomness of the sequence and enlarge the key space. In addition, the modified Logistic map presents constant chaos state with constant Lyapunov exponent under certain conditions, thus forming a robust chaotic map. Complex map can increase its Lyapunov exponent by times and can improve its initial value sensitivity and randomness.6. Based on the modified Logistic map, a chaotic encryption algorithm which can be applied to image encryption is designed. The algorithm uses the scrambling and diffusion encryption model. After the corresponding operations, the sequences generated by the modified Logistic map form the scrambling matrix and key matrix which scramble and diffuse the plaintext. The simulation experiment of the proposed algorithm is carried out with Matlab. At the same time, the relation of adjacent pixels according to the experimental results is analyzed. The results show that key space of the proposed algorithm is large and key sensitivity is strong, correlation between adjacent pixels is small and security is relatively high. It proved that the superiority of the proposed encryption algorithm based on the modified Logistic map.
Keywords/Search Tags:chaos anti-control, continuous-time system, switching system, heteroclinic loop, circuit implement, Logistic map, chaotic image encryption
PDF Full Text Request
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