近年來，隨機Poisson 跳躍系統在隨機控制領域已經吸引很多的注目。Poisson 隨機跳躍程序已經在隨機系統被用來模擬內在隨機擾動的隨機不連續跳躍行為。另外，Wiener隨機程序又稱diffusion 隨機程序代表系統內連續的隨機擾動，這些連續以及不連續的擾動是影響控制系統表現非常關鍵的因素。在這篇研究，適應性模糊控制被用在多輸入多輸出非線性帶有連續隨機擾動以及不連續隨機擾動的隨機Poisson 跳躍diffusion系統，而且H infinity的追蹤控制表現可以達到一個預設的外在擾動的消除能力。系統的結構是一個嚴格回授的形式。基於backstepping設計方法以及H infinity的控制理論，強健適應性控制被建立在多輸入多輸出非線性的隨機Poisson 跳躍系統帶有外在干擾、模糊近似誤差、估測誤差、連續以及不連續隨機擾動的影響，並且H infinity的追蹤控制表現可以達到一個預設的外在擾動的消除能力。這篇研究所提出的適應性模糊控制法則結合了H infinity 控制理論以及適應性控制理論的優點以解決強健適應性追蹤控制的問題在多輸入多輸出非線性帶有連續隨機擾動以及不連續隨機擾動的隨機Poisson 跳躍系統。另外，多輸入控制係數耦合矩陣的正定性假設也在這篇研究被放寬。最後，此篇提供兩個模擬例子，其一為數值系統，另一個為考慮隨機連續以及不連續影響的四軸機飛行系統，以驗證此篇所提出的強健適應性控制法則可以有效的控制隨機跳躍系統。

Recently, stochastic Poisson jump diffusion system has attracted much attention in stochastic control. Poisson jump process has been used to model the random discontinuous jump behavior of the intrinsic discontinuous perturbation in stochastic system. Wiener process also called diffusion process represents the continuous random fluctuation to the system. In this study, an adaptive control is introduced for multi-input multi-output (MIMO) nonlinear stochastic Poisson jump diffusion system with continuous and discontinuous random fluctuations to achieve the control performance with a prescribed disturbance attenuation level. The system structure is of a strict-feedback form. Based on backstepping design technique and control theory, robust adaptive control law is constructed for MIMO nonlinear stochastic Poisson jump diffusion system to achieve performance with a prescribed attenuation level of external disturbance, fuzzy approximation error and the effect of continuous and discontinuous fluctuations. The proposed adaptive control law combines both merits of control and adaptive control scheme to sufficiently solve the robust adaptive tracking control problem for MIMO nonlinear stochastic system with continuous and discontinuous random fluctuations. In addition, the uniformly positive definite assumption of control coefficient matrix is relaxed for MIMO adaptive control as well. The simulation results are provided to show the effectiveness of the proposed robust adaptive control law.

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