Chaos Control And Application Of Chaotic Theory In Measurement

In this paper, real-time identification and control of chaotic systems as well as applications of chaos in the measurement are studied. The primary contents include as follows: study on identifications of chaotic systems; study on variable structure control approach for controlling chaos; study on contrary-system control approach for controlling chaos; study on applications of chaos in measuring field.The primary study conclusion and innovation include the following:1.In the study on polynomial model identifications of chaotic systems, based on the relation between the error of identification model and embedding dimension, most appropriate embedding dimension is ascertained by experiment methods. The relation between the sampling periods in continuous-time chaotic systems and the error of identification model is researched.2.A nonlineary adaptive IIR Filter model for identification model of chaotic systems is presented. This model colligates the excellence which neural net model has strong nonlineary approach ability and polynomial model has faster linear approach ability. The adaptive grads arithmetic with self-governed variant step is used to follow the dynamic characteristic of the identification systems. Because the Sigmoid function is limited, it is not necessary to examine the stability of the identification systems in the adaptive process. This identification method has anti-noise ability in some degree.3.The sliding mode control method for chaotic systems based on pole-replacement is presented. A method of pole replacement is used to design the sliding mode and a exponent approaching controller is used in order to guarantee high quality of controlled systems. Theory and experiments show that this technique is robust and the equilibrium jitter can be reduced.4.The parameter-variable structure controlling to discrete-time chaotic systems is studied. The discontinue parameter-perturb is implemented to the parameter-sensitivity discrete-time chaotic systems, which perturb-parameters are respectively evaluated two invariable magnitudes on the two different side-faces of the switch-flow. When the parameter corresponding the equivalent control action isbetween the two invariable magnitudes, the approach and slide movement of the controlled systems are guaranteed.5.A new nonlinear feedback following controlling method of chaotic systems is presented to stabilize chaotic systems and follow a deterministic motion. Theory and experiments show this controlling method is strongly robust.6.The basic theory on contrary-system controlling to chaotic systems is founded.(1)The contrary-system of chaotic systems is existed in the some region of the phase space.(2) The contrary-system control method for chaotic systems can effectively control chaos. This method can control discrete-time chaos as well as continuous-time chaos. Chaotic systems can be stabled onto their fixed-points and period trajectories.(3)When the invariable coefficient filters including FIR and IIR filters are used to control chaotic systems by in-series forms, the power coefficients of the filters are irrelated as the chaotic systems and their parameters. So, it is unnecessary to know the equations of the chaotic systems and to distill some unstable period trajectories of the chaotic systems. Because the relationship between the power coefficients of the filters and target trajectories is undefined, it is impossible to define target trajectories before controlling.(4)When linear adaptive FIR filters are used to control chaotic systems, it is possible to define target trajectories before controlling. The selection of the initialization of the power coefficients of the filters and convergence factors is restricted.(5) )When nonlineary adaptive FIR filters are used to control chaotic systems, The restriction on selection of the initialization of the power coefficients of the filters and convergence factors will be weakened.7.The relevant dimension and most Lyapunov exponent of real-time measure series are calcul...