Research On Catastrophe Control Mechanism And It's Application

The found of Catastrophe theory is one of important achievements in nonlinear science. With the complication of controlled object on aeronautic and marine engineering, heavy electric power system and complex productive progress, together with the desire of performance index on controlled system becomes higher and higher. The controlling problem of complex system, especially the complex system with catastrophic characteristic, is an austere challenge the traditional control theory has to be faced with. So that new control methods are urgently required for the control problem of nonlinear catastrophe system.To adapt this actual demand, Catastrophe control theory emerges as the times require. The research of catastrophe control theory is just in its first stages, this dissertation starts with the investigation of catastrophe phenomena, catastrophe theory is introduced to control and stability analysis of system, to research catastrophe control mechanism and it's application.There are two aspects in the combination of catastrophe theory and control technology:one is to create new beneficial catastrophe while preserve all initial equilibria, named catastrophe control; another is to eliminate or restrain harmful catastrophe, called averse-catastrophe. State feedback catastrophe control method is introduced, deducing study is given both in continuous and discrete system, and simulation results confirm these methods. Washout filter based on feedback catastrophe control method is put forward, it is not only preserve the original equilibrium even under model uncertainty, but also can simplify the controller, to expand the range of control parameter.For controller always adds the dimension of controlled system, nonlinear polynomial function feedback catastrophe control method is addressed. This method can also preserve the equilibrium. The linear part can eliminate or delay the exist catastrophe to change the linear stability, while the nonlinear part can change the stability of catastrophic point, while this method can't increase system dimension.By the analysis of dive and horizontal plane nonlinear model, the catastrophe model on de dive plane is deduced, and catastrophe stability is analysized. In the horizontal plane, simplified equation is gained by center manifold theory, then draws the conclusion that the stability of limit circle arises from critical point is relate to small difference of move point and critical point. Thus,when Lypunov function cannot or is difficult to gain, one can distinguish the stability of critical point through this method.Finally, catastrophe prediction model is put forward and studied. The main catastrophe prediction model in this dissertation including: SCPC (synergetics-catastrophe prediction control) model, it can reflect the cooperative effect of all factors and catastrophe phenomenon, then predictive the time of losing stability. For strong chaos system, cell-to-cell mapping catastrophe predictive model is built, it considers the integrate effect of the nature of nonlinear dynamic and multi-variable, through the cell-to-cell map theory skillfully eliminate the effect of random initial value and inherence random of system, so it can describe the mechanism of system dynamic. Statistical cusp catastrophe predictive model is established, and the statistical analysis is applied, including parameter estimation and acceptability hypothesis test and prediction applied research, it establishs the foundation for the statistical cusp catastrophe model used in predictive control.