灰色控制系統是指只掌握或只能獲得部分控制信息的系統,通常簡稱為灰色系統。可控性和可觀測性是從控制和觀測角度表征系統結構的兩個基本特徵。
基本介紹
- 中文名:灰色系統的可控性
- 外文名:Controllability of grey system
灰色控制系統是指只掌握或只能獲得部分控制信息的系統,通常簡稱為灰色系統。可控性和可觀測性是從控制和觀測角度表征系統結構的兩個基本特徵。
定義1設 U[u1,u2,...,us]為控制向量,X=[x1,x2,...,xn]為狀態向量,Y=[y1,y2,...,ym]為輸出向量,稱
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為灰色線性控制系統的數學模型,其中![](/img/e/2b0/wZ2NnLyQmMlBzM1EzN0UmZkRjY2MDOmFzMkNDM2AzM4M2YhZzLhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
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。相應地,
稱灰色狀態矩陣,
為灰色控制矩陣,
為灰色輸出矩陣。有時候為特彆強調U,X,Y的時變性,即系統的動態特徵,也將控制向量、狀態向量、輸出向量分別記為U(t),X(t),Y(t)。
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灰色線性控制系統數學模型中的第一組方程
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稱為狀態方程,第二組方程
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稱為輸出方程。
定義2 對於給定的精度和目標向量J=[j1,j2,...,jm],若有施控裝置及控制向量U(t),通過控制輸入可使系統輸出Y(t)按要求的精度達到目標J,則稱系統是可控的。
定理1對於系統(1-1),令
則有當
時,系統可控。
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