Mutli-objective H_2 / H_∞ Optimal Controller Design by Multi-objective Genetic Algorithm for Uncertain Continuous-Time T-S Fuzzy Systems

不確定連續T-S模糊系統多目標H_2 / H_∞最佳化控制器設計

洪文壬(Wen-Ren Horng) ； 方俊雄(Chun-Hsiung Fang) ； 周至宏(Jyh-Horng Chou)

《中國機械工程學刊》 38卷2期 (2017/04) Pp. 199-209

摘要

This study presents an integration approach to synthesize non-parallel distributed compensation (non-PDC) fuzzy controller to achieve Pareto optimality of H_2 / H_∞ performance for uncertain continuous-time T-S fuzzy systems. To relax H_∞ performance condition, we employ non-quadratic Lyapunov function (NQLF) to derive the sufficient conditions and express the conditions with linear matrix inequalities (LMIs). The H_∞ performance conditions can guarantee the stability and the exogenous disturbance attenuation of controlled systems for all admissible uncertainties. In our conditions, unlike the previous proposed method, the assumption of known bounds of membership function can be alleviated. For H_2 performance, by using orthogonal function approach (OFA), we transform the finite integral performance index optimization problem to pure algebraic optimization problem. Thus mixed H_2 / H_∞ controller design problem can be represented by static optimization problem with subjecting algebraic equations and LMI conditions. Hence the design of controller can be greatly simplified. Then to search the optimal controller gain, the multi-objective genetic algorithm (MOGA) is employed. The design example is given to demonstrate the applicability of our proposed approach.

關鍵字

multi-objective optimal control ； mixed H_2 / H_∞ control ； T-S fuzzy system ； mutli-objective genetic algorithm ； orthogonal function approach ； non-quadratic Lyapunov function

並列摘要

本文旨在針對不確定連續T-S 模糊系統，提出一整合線性矩陣不等式(LMI) ，多目標基因演算法(MOGA)，正交函數法(OFA)的方法設計非平行補償(non-PDC)模糊控制器, 使系統H_2 / H_∞ 性能達到Pareto 最佳化。針對系統H_∞ 性能設計，利用非二次式Lyapunov 函數導出較寬鬆的LMI 條件，因此能保證控制系統的穩定性和外來擾動的衰減。有別於多數利用非二次式Lyapunov 函數導出的條件，在我們導出的條件中歸屬函數的導數的邊界並不需要事先預知，因此提升了條件的可行性。針對H_2 性能的設計，利用正交函數的特性，把積分型的二次性能指標轉換成代數運算的最佳化問題。因此混合H_2 / H_∞ 最佳控制器的設計便可轉換成純代數運算的限制型最佳化問題。然後利用多目標基因演算法就可搜尋其解，進而簡化了此設計問題。最後，文中也提出一範例來闡釋我們的方法。