Observer Based Uncertain Chaos Control And Chaos Synchronization

The relative problems of chaos control theory and chaos application are studied in this thesis using the methods of theoretical derivation and numerical simulation. The main achievements contained in the research are as follows:Utilizing the controlled Chen system, and according to the method of the mirror operation, the fact is found that Chen attractor is a compound structure which is obtained by merging together two simple attractors, i.e. the left-attractor and the right-attractor. By using phase space reconstruct technique from a time series, the general features of Chen system transforming from regularity to chaos are found: chaotic patterns of Chen system may emerge out of Pomeau-Manneville route and its intermittence have something to do with Hopf bifurcation and period-doubling bifurcation.Two effective observers are produced to identify the unknown parameters of uncertain Lorenz and Rossler systems respectively. Moreover, two linear feedback control strategies are proposed for controlling the two uncertain systems. Numerical simulations show that the observer can identify the unknown parameters effectively, and the proposed controllers can enable the controlled chaotic system to approach any desired points or periodic orbits.A linear state observer based synchronization scheme for a class of chaotic systems is presented, and this scheme is applied to secure communication. The analysis result shows that the system's convergence rate of the synchronization error depends on the parameter 0 of observer gain, in the sense that the larger the value of θis the faster the convergence.The chaotic encryption scheme presented by E.Alvarez in 1999 is improved: select the control parameters and the initial condition of chaotic system as the secret key, generate a bit chain Ci from the chaotic orbit, find the position at which a plaintext block appears in the Ci. Then record the number of the iterations of the chaotic map ni as the cipher block. Several weaknesses are voided in the improved scheme, which strengthens the security of the E.Alvarez cryptosystem.