應用SDRE控制技術於二階非線性系統之全域穩定度探討

Abstract

本論文探討二階非線性系統使用SDRE控制技術之全域漸近穩定性議題。首先，本論文提出使用固定狀態相關係數（state-dependent coefficient，SDC）矩陣表示式無法達到全域漸近穩定之例子。接著本論文針對二階非線性可控系統經由適當的選取SDC矩陣提出使用SDRE控制策略能達到全域漸近穩定之條件。之後本論文也將SDRE控制策略全域漸近穩定之議題推廣至更廣義的二階非線性系統，並經由SDC參數的選取將系統轉變成逐點 (pointwise) 線性可穩定但不可控的型式。最後，示範如何使用以及成功應用分析的結果。

This thesis investigates the globally asymptotic stability (GAS) issues regarding a class of second order nonlinear systems using the state-dependent Riccati equation (SDRE) control scheme. First, we present an example with the SDRE scheme and a specific state-dependent coefficient (SDC) matrix representation such that the origin is not GAS. Next, by selecting suitable SDC matrices, a condition that makes the origin of a second order controllable nonlinear system GAS by the SDRE scheme is presented. Moreover, the GAS issue is extended to a more general second order systems which is transformed to be pointwisely stabilizable but not controllable through appropriate selection of SDC parameters. Finally, illustrative examples are given to demonstrate the use and the success of the analysis.