結合局部搜尋之多目標並行處理粒子群聚最佳化法及其在不確定間隔系統數位控制之應用(3/3)

Abstract

連續時間間隔系統(continuous-time interval systems)之數位控制(digital control)係一 不易藉由傳統方法處理的問題，為了替這種系統進行數位模擬(digital simulation)或是數 位設計(digital design)，在數位化(discretization) 的過程中會導致數位模型係數為不確定 參數之非線性函數，而且有嚴重地指數函數耦合情況，這使得原系統之間隔結構(interval structure)在數位化的過程中喪失殆盡；同時，在數位化的過程中也會額外引進一獨立變 數-取樣時間 (sampling period)，使得數位控制系統之分析及設計更加困難。這些複雜的 問題至少包含：連續時間間隔系統之數位建模 (discrete modelling)、等效數位模型最小 相條件 (minimum-phase criteria)、數位控制器之設計(Digital redesign of continuous systems with improved suitability)、數位化再設計之性能評估(Performance evaluation of redesigned digital system for uncertain interval systems)等。有鑑於這些問題所要處理的函 數大都為高度非線性耦合(nonlinear coupling) 之non-convex 函數，傳統最佳化方法將無 法有效解決此一問題，特別是在處理高階的間隔系統時尤其困難，因此，本計劃即針對 該些問題提出可能之解決方案，作法上係藉由對不確定參數作適當的邊界跳脫 (overbounding)，將求取等效數位模型、最小相取樣時間範圍、穩定取樣時間範圍、以及 數位化再設計之適合度評估等問題，規劃形成複數個最佳化的問題，再利用所提出具有 並行處理能力的通用型(general-purpose)、嵌設有改良式NM 區域搜尋法、以及加入多目 標最佳化處理機制等功能之粒子群聚最佳化法之研究成果為基礎，發揮其全域最佳化、 概念簡單、容易實現、高運作效能等優點、具備並行處理能力之優勢，以改善粒子群聚 最佳化法的演化過程較為耗時的問題，提升其運算效能，以有效解決上述不確定連續時 間間隔系統在數位控制之分析及設計上之諸多問題，方便使用者應用離散時間領域中關 於強健控制之既有方法，進行後續之的分析與設計。

Problems relevant to digital control of uncertain interval systems are generally regarded difficult to deal with by conventional methods because the coefficients of the discrete model depend nonlinearly on the uncertain parameters after the discretization process. An independent variable, sampling time T, is also introduced during the discretization process, which imposes extra difficulties in the analysis and design of the digital control system. These problems at least include: discrete modelling of uncertain interval plant, minimum-phase criteria for discrete-time equivalent model of uncertain interval systems, Performance evaluation of redesigned digital system for uncertain interval systems digital redesign of continuous systems with improved suitability, and performance evaluation of redesigned digital system for uncertain interval systems, etc. Because of non-convex nature of the coefficient functions in the discretized system, conventional optimization methods, such as gradient-based methods, fail to obtain satisfactory results, particularly for systems with higher order. It is therefore the objective of this project to solve these problems by considering the worst-case situation of the discrete model via an overbounding process. By suitably formulating the problems under consideration into multiple mono-objective optimization problems, the proposed universal PSO optimizer incoporating a NM local search scheme with parallel computation capability can be used to derive an equivalent discrete interval model enclosing the exact uncertain discrete model, determine a sampling-time range for either ensuring minimum-phase condition or stability of the digital control system, and evaluate suitability analysis of the redesigned digital system. The solutions to the above-mentioned problems, once completed by this project, will assist existing robustness results in the discrete-time domain for further analysis and design of sampled-data control systems.