仿射非線性系統之適應性最佳順滑模控制器

Abstract

本篇論文採用適應性最佳控制法求解仿射非線性系統順滑模控制器設計的問題，藉由適應性最佳控制法優化順滑模控制的等效控制訊號求得最佳控制器參數。傳統非線性系統的順滑模控制器設計多利用線性化求解，而線性化會降低控制精凖度且不適用於高度非線性的系統，適應性最佳控制的特點是可以依照指定的成本函數優化控制器，使用者可選擇特定的成本函數來規劃系統軌跡進入順滑模態後的系統響應行為，適應性最佳控制法把最佳控制的極小值原理的逆向演算轉換為順向循序演算的強化學習機制，以此架構來循序優化各類型的非線性控制器。本論文針對仿射非線性系統提出最佳順滑模控制器的設計方法，在離散型順滑模控制器的等效控制設計當中，導入適應性最佳控制法，透過循序優化的強化學習機制來優化等效控制的參數，實現仿射非線性系統之適應性最佳順滑模控制器的設計，透過例題的電腦模擬來驗證此求解方法的成效，其結果顯示適應性最佳控制法確實可以透過學習程序來循序優化控制器參數，使成本函數趨近極小值，求得仿射非線性系統的順滑模控制器的近似最佳解。

This thesis presents an adaptive optimal control algorithm (AOCA) dedicated to solve the optimal sliding mode control problems of affine nonlinear systems by sequential optimization. Concerning with sliding model control of nonlinear systems, designers are used to linearize the system model about an operating point in order to solve for the sliding mode controller under linear environment. However, the linearization may introduce large model error while shifting between operating points that, as a result, leads to bad control performance or even fails to work in systems with severe nonlinearity. In contrast, the AOCA deals with the nonlinear model directly to optimize the equivalent control law in terms of minimizing a specified cost function. The AOCA organizes the optimality conditions derived from the minimum principle in the architecture of reinforcement learning to achieve sequential optimization. The proposed design is dedicated to use in affine nonlinear systems, and the effectiveness has been investigated in several bench-mark examples by computer simulations. The results show that the design can find out the optimal equivalent control laws of sliding model control systems.