The robust control of human arm movements is planed according to the integration of sensory information, sensory motor transformation and human brain computation. The human arm is controlled to an acceptable posture in a robust optimal way. Due to the intelligent nature of human judgments, the application of Takagi-Sugeno (T-S) fuzzy model to human judgments is appealing to emulate the intelligent computation in the prefrontal cortex of human brain in the sensorimotor control of human arm movement. Here, we try to apply a robust fuzzy estimator-based control scheme to mimic the sensorimotor control of realistic planar movement of the human arm. However, the state variables of the planar model of the human arm are not all available via visual and proprioception information. With the help of posture (state) estimation based on human sensory information in human brain, a robust fuzzy estimator-based control is introduced for sensorimotor reference tracking control of arm movement in spite of internal noises, state-dependent noises, environmental noises and uncertain initial values. Based on fuzzy interpolation for nonlinear stochastic arm system, the complicated noise-tolerance robust control of human arm tracking problem can be simplified by solving a set of linear matrix inequalities (LMIs) through Newton’s iterative method via an interior point scheme of convex optimization. Finally, a simulation example is given to illustrate the control procedure and confirm the performance of the robust fuzzy estimator-based sensorimotor control for human arm system.

人類手臂移動的強健控制是由感測資訊、感測運動轉換和大腦決策來規劃。人類手臂是由強健最佳化的方式被控制到可接受的姿態。由於大腦決策是不精確的且具模糊特性，模糊理論的概念在大腦決策上可被應用於人類手臂移動控制時大腦中前額葉皮質區的思考決策過程。在此篇研究中我們試著應用強健控制器的設計方法模仿人類手臂實際移動控制的過程。然而在手臂的動態模型中經過人的視覺和本體感覺的量測並非所有狀態都可被獲得，在人類大腦中藉由人體感測的訊息可以估計肢體的各個狀態，藉由大腦對肢體狀態估測的訊息，強健模糊具觀測基礎的控制被提出在各種狀態或控制訊號相關聯的雜訊環境中被應用，此種雜訊包含了人類體內內部雜訊、和各個肢體狀態或角度相關的雜訊和由外在環境的變化造成的雜訊。為了解決複雜具雜訊容忍的強健控制器設計問題T-S fuzzy model和線性矩陣不等式被應用來簡化設計過程，利用T-S fuzzy model不僅是可以把原本要解很複雜的Hamilton Jacobian Inequality問題變成簡化成只要解一般的線性矩陣不等式問題而且可以模仿大腦的聰明思考判斷的過程，因為電腦在解線性矩陣不等式的過程是利用牛頓疊帶法在convex最佳的內部點中搜尋出所要的參數，這個過程就像人類訓練和學習的過程。最後用一個例子來說明設計流程及驗證我們的強健控制器設計的效能。

中文摘要……............................................................................................................... i
Abstract ........................................................................................................................ ii
Contents ...................................................................................................................... iv
List of figures ............................................................................................................... v
List of tables ................................................................................................................. v
1 Introduction .......................................................................................................... 1
2 Methods ................................................................................................................. 6
2.1 Stochastic planar model of the human arm with 2 joints and visual observation ...................................................................................................... 6
2.2 Robust H∞ estimator-based sensorimotor control of a stochastic 2-link human arm system via fuzzy computation method ................................................... 19
3 Computational Simulations .......................................................................... 29
4 Discussion and Conclusion ................................................................................ 38
5 Appendix ............................................................................................................. 41
5.1 Appendix A. Proof of Proposition 1 .............................................................41
5.2 Appendix B. Proof of Proposition 2..............................................................42
5.3 Appendix C. Decoupling processes of (23) ..................................................43
5.4 Appendix D. Proof of Lemma 1....................................................................45
Bibliography ............................................................................................................. 46

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