Nonlinear Observers, Normal Forms and Model Reduction

这项建议是为了研究几种很有前途的设计非线性控制系统观测器的新方法，包括状态误差动态线性化、反推和多扩展卡尔曼滤波。为了确定哪种类型的观测器适合于给定的非线性系统，需要对可能性的范围进行分类。因此，还提出了一种适合于观测器设计的非线性系统在群体作用下的范式的研究。控制系统是真实世界过程的数学模型。它有输入和输出，用来模拟系统与外部世界交互的方式，并有状态变量，描述系统的内部存储器。状态按照某种由输入驱动的动力学模型演化，输出是状态的某种函数，也可能是输入的函数。控制系统的基本问题是以一种稳定的方式闭合回路。我们希望使用基于当前状态的负反馈来将系统稳定到某种理想的运行状态。但通常情况下，当前状态是不可直接测量的，所以我们必须设计一个观测器来根据过去的输入和输出来估计它。非线性观测器设计方法的发展是系统理论及其应用的一个重要问题。目前还没有一种方法对所有的非线性系统都有效。

0204390KrenerThis proposal is for research on several promising new approaches to designing an observer for a nonlinear control system, including linearization of the state error dynamics, backstepping and multiple extended Kalman filters. In order to decide which type of observer is appropriate for a given nonlinear system, one needs a classification of the range of possibilities. Therefore a study of the normal forms of a nonlinear system under a group action that is appropriate to observer design is also proposed.A control system is a mathematical model of a real world process. It has inputs and outputs which model the way the way the system interacts with the external world and has state variables, which describe the internal memory of the system. The state evolves according to some dynamical model driven by the inputs and the output is some function of the state and possibly the input. The fundamental problem of control systems is to close the loop in such a way as to achieve stability. We wish to use negative feedback based on the current state to stabilize the system to some desirable operating regime. But usually the current state is not directly measurable so we must design an observer to estimate it from the past inputs and outputs. The development of nonlinear observer design methodologies is a paramount problem of systems theory and its applications. There is no current approach that is effective for all nonlinear systems.