【正文】 l 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 adaptive control system, the optimal control system for, learn to control system, etc. Recently, nonlinear adaptive control system based on neural network adaptive control and get attention, and put forward some new methods.4. Robust Control (Robust Control)Process control is an important issue facing is model uncertainty, robust control mainly to solve the model uncertainty problem, but in processing method and adaptive control different. Adaptive control of basic idea is to carry out the model parameter of identify, and then to design the controller. Controller parameters adjustment depends on the renewal of the model parameters, not in possible uncertainty into consideration. And robust control in design as far as possible when the controller using uncertainty information to design a controller, making the uncertain parameters appear still could satisfy the performance requirements.Robust control think of the uncertainty of the system can be used to describe the model collection system, the model is not only, can be a model of any one of the elements in the collection, but in the controller design, can make the model collection of elements meet the requirements. Robust control of a major problem is robust stability, now monly used in three ways:(1) When the system is studied with state matrix or features polynomial algebra in description generally USES the method, the center is to discuss the problem or matrix of the stability of polynomial problem。(2) Iyapunov method of uncertainty to state space model appear is a useful tool。 (3) frequency domain method from the transfer function of the research question, typically Hoo control, it used as a robust effectiveness of analysis reflected in external disturbance that no longer for fixed, and only request energy bounded can. This method has been used in engineering design, such as Hoo optimal sensitivity controller design.5. Fuzzy Control (Fuzzy Control)Fuzzy control with fuzzy mathematical simulation of people thinking method, the process of the operator experience summarized, use the language variables and fuzzy logic theory reasoning and decisionmaking, plex object to control. Fuzzy control is not mean to be accused of process is fuzzy, that doesn39。t mean the controller is not set, it is the concept of knowledge and said the fuzziness, it pleted work is entirely sure.In 1974 the British engineer for the first time amdam the Fuzzy set theory for the boiler and steam machine control since, opened up a new field of Fuzzy control, especially for large delay and nonlinearity is hard to develop practical mathematical model of plex system, through the puter to realize Fuzzy control often can obtain very good results.The type of fuzzy control are:(1) Basic fuzzy controller, once the fuzzy control table was determined, control rule is fixed。 (2) the adaptive fuzzy controller, in operation of automatic modification, perfect and adjust the rules, that was accused of process control effect is improved, and achieve the desired effect。(3) Intelligent fuzzy controller, which, artificial intelligence and neural network linked to three, to realize prehensive information processing, make the system not only has the flexible reasoning mechanism, heuristic knowledge and production rules said, and has many layers, various types of control laws of choice.The characteristics of the fuzzy control is not to need to accurate mathematical model, robust, the control effect is good, easy to overe the influence of nonlinear factors, the control method is easy to grasp. Recently, someone put forward fuzzy neuralInter3 fusion control model, that is, the fusion structure, fusion algorithm and control is an organic whole to carry on the design. Again someone proposed by homotopy BP network memory fuzzy rules to lenovo way use these experience. Fuzzy control problems to be further studied: the fuzzy control system function, stability, optimization evaluation。 Complicated nonlinear system of f