Studies on the Design of Simple Adaptive Control (SAC) Systems for Nonlinear Systems

常系数线性系统的几乎严格正实(ASPRness)是存在使闭环系统传递函数为严格正实的静态输出反馈的充分条件。换言之，通过一种简单的基于输出的控制算法就可以稳定ASPR对象。简单自适应控制(SAC)是一种基本的自适应控制算法，它结合了ASPR和指令发生器跟踪器理论，广泛应用于实际控制系统的设计中。然而，关于非线性自适应控制系统的理论研究成果很少。在研究报告中，提出了一种基于输出反馈无源性的非线性自适应控制系统设计的统一方法，该无源性对应于线性系统的ASPR性。对非OFP对象的情况也进行了处理，这对应于在线性对象上安装并联反馈补偿器。几种实用的自适应控制系统设计方法也被认为是基于OFP的自适应控制系统设计的相关问题。

Almost strict positive realness (ASPRness) at constant coefficient linear systems is a sufficient condition for the existence of a static output feedback that makes the closed-loop transfer function be strictly positive real. In other words, it is possible to stabilize ASPR plant by a simple output-based control algorithm. Simple adaptive control (SAC) is a basic adaptive control algorithm by combining ASPRness and command generator tracker theory and it is widely used for practical control system design. However, as to nonlinear SAC systems, there have been few theoretical results.In the research report, a unified approach for the design of nonlinear SAC system based on the output feedback passivity that corresponds to the ASPRness in the linear system. The case of non-OFP plant is also treated which corresponds to the install of parallel feedback compensator at linear plants. Several practically useful design methods of adaptive control systems are also considered as a related problem of OFP based adaptive control system design.