Adaptive control of nonlinear systems and applications

一些物理系统用常微分方程组(ODE)建模，而另一些物理系统则必须用微分代数方程(DAE)描述。通常，DAE系统是对许多实际流程的基本描述，而ODE系统是一个简化。某些DAE系统可以简化为ODE系统。在大多数情况下，这样的简化是无法实现的。因此，对DAE系统的研究与对ODE系统的研究同样具有重要意义。几乎所有的物理系统本质上都是非线性的，并且包含一定数量的未知参数。因此，发展一种非线性控制理论，对于构造控制器以实现控制目标和设计自适应律以估计未知参数具有重要的理论和实际意义。自20世纪70年代以来，自适应控制一直受到控制专家的高度关注。对于线性系统，自适应控制理论已经得到了很好的建立，而对于非线性系统，自适应控制理论还远远不够完善。现有的所有自适应控制设计方法都有其局限性。本研究的第一个目标是改进现有的自适应控制器设计方法，寻找新的设计方法。显然，线性DAE系统的控制理论已经很好地建立起来了。关于非线性DAE系统反馈控制的文献很少。据申请人所知，DAE系统的自适应控制问题仍然悬而未决。该研究计划的第二个目标是发展一种非线性DAE系统的自适应控制设计方法。他说，很明显，控制理论和工程领域存在很大差距。第三个目标是研究非线性自适应控制在机器人、电机、电力电子变流器等方面的应用，以缩小自适应控制理论与应用之间的差距。他说，该方案的意义在于可能在非线性DAE系统的自适应控制理论和自适应控制理论的应用方面取得突破。

Some physical systems are modeled by ordinary differential equations (ODE), while others must be described by differential algebraic equations (DAE). In general, DAE systems are the basic description of a number of practical processes while ODE systems are a simplification. Some DAE systems can be reduced to ODE systems. In most cases, such a simplification is not realizable. Therefore, the study of DAE systems is as significant as ODE systems. Almost all physical systems are nonlinear in nature and contain a certain amount of unknown parameters. Therefore, it is of both theoretical and practical importance to develop a nonlinear control theory for constructing controllers to achieve the control objectives and designing adaptive laws to estimate unknown parameters.     Adaptive control has been drawing great attention from control experts since the 1970s. For linear systems, the adaptive control theory has been well established, while it is far from perfect for the nonlinear counterpart. All existing adaptive control design methods have their limitations. The first objective of this research program is to improve the existing adaptive controller design methods and search for a new design technique.     The control theory of linear DAE systems has been well established. The literature on feedback control of nonlinear DAE systems is sparse. To the best of the applicant's knowledge, the adaptive control problems for DAE systems is still open. The second objective of this research program is to develop a design method for adaptive control of nonlinear DAE systems.     It is obvious that there exists a big gap between the control theory and engineering fields. The third objective is to investigate the applications of nonlinear adaptive control to robots, motors, power electronics converters, and so on, to reduce the gap between the adaptive control theory and applications.     The significance of this program lies in a possible breakthrough in the adaptive control theory for nonlinear DAE systems and applications of adaptive control theory.