PYIA: Nonlinear Control Systems

本研究计划的主要目标是发展非线性动态系统的非线性数字控制器的设计方法。由于控制器结构的选择高度依赖于底层系统的结构特性，因此第一步将是通过引入通常的取样保持装置来确定连续时间系统的几何特性是如何变形的。作者和他的学生最近的工作已经澄清了线性情况，但对于非线性系统，还有很多工作要做。然而，初步结果表明，通过允许多速率采样获得的额外灵活性对于实现反馈线性化等设计目标至关重要；我们将进一步开展第二种调查途径。第三个目标是发展一个离散时间非线性系统的“传递动力学”的概念；这将起到线性系统的传输零点的作用，并将导致控制器同时解耦和稳定非线性离散系统的存在条件。最后，将与法国的穆格（C. Moog）博士和意大利的贝内代托（M. di Benedetto）博士共同研究用于分析非线性系统的微分代数工具。本研究的主要目的是发展非线性动态系统的非线性数字控制器的设计方法。该研究对高性能非线性系统的控制具有重要的指导意义。

The main objective of this research program is to develop methodologies for the design of nonlinear digital controllers for nonlinear dynamic systems. Since the choice of a controller structure is highly dependent upon the structural properties of the underlying system, the first step will be to determine how the geometric properties of a continuous-time system are deformed by the introduction of the usual sample-and-hold devices. Recent work of the author and his students has clarified the linear case, but for nonlinear systems, much work remains to be done. However, preliminary results show that the additional flexibility gained by allowing multi-rate sampling is crucial to achieving such design goals as feedback linearization; this second avenue of investigation will be further pursued. A third goal will be to develop a notion of "transmission dynamics" of a discrete-time nonlinear system; this will play the role of the transmission zeros of a linear system and will lead to conditions for the existence of controllers which simultaneously decouple and stabilize a nonlinear discrete-time system. Finally, joint work will be done with Dr. C. Moog, of France, and Dr. M. di Benedetto, of Italy, on differential algebraic tools for the analysis of nonlinear systems. The main objective of this research is to develop methodologies for the design of nonlinear digital controllers for nonlinear dynamic systems. This research will be valuable in controlling high performance nonlinear systems such as those encountered in advanced aircraft and process control.