外文翻译：现代控制理论的发展(编辑修改稿)

外文翻译：现代控制理论的发展(编辑修改稿)内容摘要：

a very difficult question, Taylor series development for some situation is not applicable. The classical theory of the phase plane law only applies to the second order systems, apply to contain a nonlinear element of high order system describing function method is also a kind of approximate method. Because of the lack of nonlinear system research system, the general theory and methods, and prehensive methods to get bigger development, basically have: (1) The lyapunov method: it is by far the most perfect, the most general nonlinear method, but because of its general, used to analysis the stability or used to calm when lack structure are prehensive sex. (2) Variable structure control: because its sliding mode has to interfere with the perturbation, j, to the 8039。 s attention, is a kind of practical nonlinear control of the synthesis method. (3) Differential geometry method: in the past 20 years, differential geometry method, nonlinear control systems research has been the mainstream, it to nonlinear system structure analysis, deposition, and structure of the relevant control design bring great convenience. Use the method of differential geometry nonlinear system is the inevitable oute of the development of modern mathematics, as Italy isidori professor pointed out: with differential geometry nonlinear system method to study the achievements, like 50 s with the Laplace transformation and plex function theory to single input and single output system research, or with linear algebra to multivariable systems research. But this approach also has its shortings, reflected in its plexity, without the hierarchy, the accurate linear control and spatial measure is destroyed, etc. So recently and scholars, the introduction of new more profound mathematical tools to develop new direction, for example: differential dynamics, differential topology and algebra topology, algebra how a few. 3. Adaptive Control (Adaptive Control) Adaptive control system by constantly measuring system of input, the state, output or performance parameters, and gradually to understand and grasp object, and then according to the information obtained according to certain design method, make decisions to update the controller39。 s structure and parameters to adapt to the change of environment, to reach the required control performance indicators. Adaptive control system should have three basic functions: (1) Identification of the object structure and parameters so as to accurately established the mathematical model of the controlled objects。 (2) Given a control law in order to make the controlled system reach the expected performance index。 (3) To be automatic correction controller parameters. So the adaptive control system is mainly used to process model unknown or process model structure known but unknown parameters and the random system. Adaptive control system of main type is used for the control system, the model reference adaptiv。