This study addresses the robust H_infinity filter and control design problems for nonlinear stochastic partial differential systems (NSPDSs) with Poisson noise under the environment of random external disturbance and measurement noise in the spatio-temporal domain. For NSPDSs, the robust H_infinity filter and control designs via a set of sensor measurements need to solve a complex Hamilton Jacobi integral inequality (HJII) for robust estimation and control despite random external disturbance and measurement noise. In general, it is very difficult to solve the nonlinear partial differential HJII. In order to simplify the design procedure, a fuzzy stochastic partial differential system is proposed to approximate the NSPDS based on fuzzy interpolation approach. Then a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semi-discretization finite difference scheme and the Kronecker product. Based on this model both robust H_infinity filter and control designs are proposed to achieve the robust estimation and control via solving linear matrix inequalities (LMIs) instead of an HJII. The proposed robust fuzzy H_infinity filter and controller have an efficient ability to attenuate the effect of spatio-temporal external disturbance and measurement noise on the estimation and control of NSPDSs from the area energy point of view. Finally, some robust H_infinity estimation and control examples are given for the illustration of design procedure and the performance confirmation of the proposed robust filter and controller design methods.

本篇研究乃是針對一些含有波松雜訊(Poisson noise)的非線性隨機偏微分系統，處在時空領域上的任意外界擾動和測量雜訊的環境下，提出一個強健 濾波器及控制的設計問題。對於非線性隨機偏微分系統而言，經由一組感測器來設計濾波器及控制，必須求解一個無論在任意外界擾動和測量雜訊下，能夠達到強健估測及控制之相關的複雜漢彌爾頓-傑克比積分不等式(Hamilton Jacobi integral inequality)。一般而言，是很難以求得這種非線性偏微分漢彌爾頓-傑克比積分不等式的解。因此，為了要簡化設計程序起見，一個根基於模糊內插方法的模糊隨機偏微分系統是被提出來近似非線性隨機偏微分系統。然後，藉著採用半離散化的有限差分法和克羅內克乘積(Kronecker product)，一個模糊隨機空間上的狀態空間模型就被發展出來以表示模糊隨機偏微分系統。基於這個空間上的狀態空間模型，藉由求解線性矩陣不等式以取代求解漢彌爾頓-傑克比積分不等式，一個強健 濾波器及控制的設計是被提出來，以獲得強健估測及控制。從區域能量的觀點來看，這個被提出的強健H_infinity濾波器及控制器能有效率地減少時空領域上的外界擾動和測量雜訊對於非線性隨機偏微分系統的估測及控制上的影響。最後，給予一些強健H_infinity估測及控制的例子，來說明設計的步驟並且肯定這個所提出的強健濾波器及控制器的設計之效能。

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