本文提出兩種以粒子群聚最佳化法為基礎之混合式演算法，分別與NM單體搜尋法(NM-PSO)以及中心粒子群聚演算法(NM-PSO-C)做結合，針對多階最佳化問題找到最有可能的全域最佳解。 在控制系統方面，我們以PSO演算法為基底，應用在解決不確定間隔系統數位化再設計的問題。作法上係對數位控制器參數作實數編碼後，再與不確定連續時間間隔系統數位化後之模型作結合，以閉迴路數位系統之性能做考慮，並分別以數位再設計系統頻率響應封包圖以及極值系統之增益/相位邊限的相似度為適合度評定機制之指標，藉由與其相對應之類比系統做比較，據以調整數位控制器的參數，使數位化再設計系統之性能能夠接近原類比系統。 This paper proposes hybrid optimization approaches incorporating particle swarm optimization with the use of a center particle in a swarm and an enhanced Nelder-Mead simplex search method to solve multi-dimensional optimization problems.
Thanks to the performance of the proposed optimizer, PSO-based approaches are presented to derive optimal digital controllers for uncertain interval systems based on resemblance of extremal gain/phase margins (GM/PM) and frequency-response, respectively. By combining the uncertain plant and controller, extremal systems of the redesigned digital system having an interval plant and its continuous counterpart can be obtained as the basis for comparison. The design problem is then formulated as an optimization problem of an aggregated error function in terms of deviation on extremal GM/PM and frequency-response between the redesigned digital system and its continuous counterpart, and subsequently optimized by the proposed optimizer to obtain an optimal set of parameters for the digital controller.
