Chaos Control For Several Chaotic Systems And Bifurcation Analysis In Single-Stage PFC Power Supplies

Nonlinear science has received great development in past decades, it is a fundamental subject investigating the common characteristic of nonlinear phenomena and is considered as "one of the three revolutions" of the twentieth century in natural science. Generally speaking, nonlinear science contains chaos, bifurcation, fractal, soliton and complexity as its five main parts.Since E.N.Lorenz found the first classical attractor in 1963, chaos has attracted considerable interest in many domains . There are many purposes to study chaos theoretically, such as to bring out its essence,to describe its fundamental characteristics, to acquire its dynamics and to control it so as to put it into application.In past years, many techniques and theories have been developed to control and synchronize chaos. Today, the concepts of stability and chaos are commonplace in the scientific community. Stability is a classical subject, whereas chaos is a recent field. There is one class of mechanisms that control both, namely, bifurcations. Solutions of nonlinear equations bifurcate at critical values of system parameters. At these bifurcation points, stability may be lost or gained. On the other hand, chaos sets in after a sequence of certain bifurcations. The wide range of states, with equilibrium as the most rigid state and chaos as the most flexible state, is governed by bifurcations. Bifurcations form the machinery of structural changes. In the field of nonlinear science, research on chaos and bifurcation has become a leading issue.This paper further investigates the control and synchronization for the Lorenz systems family , it also studies some bifurcation phenomena in power electron-ics.Altogether there are eight chapters, and can be divided into two parts according to the basic content.The first part systematically investigates chaos control and synchronization for the newly advanced Lorenz systems family and a new discrete iterative chaotic system discovered in the study of evolutionary algorithms.The main contents and innovation points are listed as follows.1) Backstepping design is proposed for controlling uncertain Lü system based on parameter identification[49]. This method is applied to identify the unknown parameter of the Lü system and then control it to bounded points. Furthermore,it can track any continuous or discrete target. Especially, the control law designed avoids the divergence of l/x and l/rc2[48]. For completely uncertain Lu system, adaptive backstepping method is also applied to achieve parameter identification and control simultaneously with one or two controllers[50], which improves and extends the work in [51, 52].2) Synchronization with a single driving variable is investigated to sychro-nize a unified chaotic system. Several sufficient conditions are gained. A scheme of secure communication based on this synchronization is produced, numerical simulations are provided to verify its feasibility[53].Linear feedback synchronization and adaptive feedback synchronization with only one controller for the unified chaotic system are also discussed, and two syhchronization theorems are obtained, which also improves the work of Wang et al[55].3) Sampled-data feedback control is proposed for the unified chaotic system[57], the robustness of this method is verified; Occasional driving is also used to synchronize the unified chaotic system, the relation among interim period,sampling interval,feedback gain and the system parameter is thoroughly investigated[59]; Impulsive control and synchronization for the Lorenz systems family is further investigated, some more comprehensive and less conservative criteria for exponential stability and asymptotical stability are established. In particular, some simple and easily verified sufficient conditions are derived with equivalent impulse intervals.4 )A non-autonomous unified chaotic system with continuous periodic switch between the Lorenz and Chen systems is presented for the first time [60]. It displays abundant dynamics. The linear feedback control and tracking of any target function are designed. Based on this system, we further put forward a unified chaotic system with delayed continuous periodic switch and study its dynamic behavior. Also, with a time-delay feedback technique, we can find many unstable periodic orbits and stabilize them. [61].5) A new discrete chaotic system with rational fraction is first introduced, which was discovered in evolutionary algorithm. The dynamical behaviors, period-doubling bifurcation and Lyapunov exponents spectrum are further investigated. Moreover, we study the tracking and control problems of this new system[63].In the second part, we investigate the bifurcation phenomena in a single-stage power-factor-correction converter in power electronics. Due to its practical versatility in power applications, this circuit has received a great deal of attention in the past decade[88]-[90]. However, previous studies have mainly focused on the steady-state design and control aspects of this circuit, and the detailed dynamical behavior and stability boundaries have not been thoroughly pursued, not to mention theoretical analysis. We report fast-scale period-doubling bifurcation in the complete single-stage PFC power supply using numerical simulations,then verify the phenomena by theoretical analysis and experimental verifications.The results will facilitate the selection of practical parameter values for maintaining stable operation.The main innovation points of this paper are listed above. As an integral thesis, it also contains the historical background, research progress, relative results in this field, and the prospect for future study.