本文章將探討如何將H∞ 強健控制導引律進行動力分配，將期望控制力合理的分配至船體上各個致動器，推導出致動器控制命令並實踐於一艘正在開發中的魚雷型水下載具。首先觀察並研究開發中的水下載具之致動器種類、數量以及在船體的位置，藉由實驗或是程式模擬蒐集各個致動器的輸入輸出資料並且透過線性近似或是類神經網路的方法來建立各個致動器之數學模型，再者根據致動器在船體的位置建立船體致動器的動力轉移矩陣並計算其秩，判斷船體可控制的維度。H∞ 強健控制推導出的控制力，將利用最小平方法與二次線性規劃法依據船體致動器的動力轉移矩陣分配至船上的各個致動器，各個致動器依照動力分配結果透過各自的致動器模型計算出控制命令。計算出的控制命令將會輸入至開發中的魚雷型水下載具的數學模型中驗證動力分配的結果。

The control allocation for the H∞ robust control laws on the developed torpedo-like underwater vehicle is implemented in this article. The goal of the study is to distribute the desired control law to each actuator on the underwater vehicle and derive the control command for all the actuators within their limitations. The first step of the control allocation is observing the types, numbers, positions of the actuators installed on the developed underwater vehicle. Then collect the input and output data of each actuator through experiment or program simulation and construct the mathematical model of each actuator by applying the linear approximation or neural network on the gathered data. Furthermore, build up the thrust configuration matrix of the underwater vehicle by the locations of the actuators and calculate its rank to clarify the degree of freedoms that the underwater vehicle is capable of controlling. The desired control laws derived by H∞ robust control is distributed to actuators using the least square optimization method and quadratic programming method and the control commands of each actuator are calculated through the constructed actuator models. Two simulations of different initial state are presented in the article to show how the proposed control allocation process performs.

[1] M. Chachada, L. Vachhani, and V. Kartik, "Empirical waypoint navigator for overactuated autonomous underwater vehicle using novel kinematic-dynamic controller pair and control allocation techniques," 2016 Indian Control Conference (ICC), pp. 354-361, 2016.
[2] C. S. Chin, M. W. S. Lau, E. Low, and G. G. L. Seet, "A cascaded nonlinear heading control with whrust allocation: An application on an underactuated remotely operated vehicle," 2006 IEEE Conference on Robotics, Automation and Mechatronics, pp. 1-6, 2006.
[3] S. Ji, J. Jang, J. Jeong, and Y. Kim, "The H∞ controller design including control allocation for marine vessel," 2012 12th International Conference on Control, Automation and Systems, pp. 1905-1907, 2012.
[4] C. Shen, Y. Shi, and B. Buckham, "Lyapunov-Based model predictive control for dynamic positioning of autonomous underwater vehicles," 2017 IEEE International Conference on Unmanned Systems (ICUS), pp. 588-593, 2017.
[5] C. Yu, X. Xiang, P. A. Wilson, and Q. Zhang, "Guidance-Error-Based Robust Fuzzy Adaptive Control for Bottom Following of a Flight-Style AUV With Saturated Actuator Dynamics," IEEE Transactions on Cybernetics, vol. 50, no. 5, pp. 1887-1899, 2020.
[6] T. A. Johansen and T. I. Fossen, "Control allocation - A survey," Automatica, vol. 49, pp. 1087-1103, 2013.
[7] M. W. Oppenheimer, D. B. Doman, and M. A. Bolender, "Control Allocation for Over-actuated Systems," 2006 14th Mediterranean Conference on Control and Automation, pp. 1-6, 2006.
[8] H. Z. I. Khan, J. Rajput, S. Ahmed, M. Sarmad, and M. Sharjil, "Robust control of overactuated autonomous underwater vehicle," 2018 15th International Bhurban Conference on Applied Sciences and Technology (IBCAST), pp. 269-275, 2018.
[9] S. Soylu, B. J. Buckham, and R. P. Podhorodeski, "Robust control of underwater vehicles with Fault-Tolerant Infinity-Norm thruster force allocation," OCEANS 2007, pp. 1-10, 2007.
[10] Z. Yinghao, Z. Jiangfeng, L. Yueming, S. Yushan, W. Lei, and H. Shuling, "Research on reconstructive fault-tolerant control of an X-rudder AUV," OCEANS 2016 MTS/IEEE Monterey, pp. 1-5, 2016.
[11] A. Tolstonogov and V. Kostenko, "AUV thrust allocation with variable constraints," ASSA, vol. 17, no.3, pp. 1-8, 2017.
[12] T. I. Fossen and T. A. Johansen, "A survey of control allocation methods for ships and underwater vehicles," 2006 14th Mediterranean Conference on Control and Automation, pp. 1-6, 2006.
[13] T. Fossen, T. Johansen, and P. Tristan, "A survey of control allocation methods for underwater vehicles," Underwater Vehicles, pp. 110-128, 2009.
[14] Y. Yi-Sheng, "Design of adaptive fuzzy guidance law for autonomous underwater vehicles : Mixed H2/H∞ approach," NCKU, pp. 1-92, 2020.
[15] X. Gao and L. Liao, "A new one-layer neural network for linear and quadratic programming," IEEE Transactions on Neural Networks, vol. 21, no. 6, pp. 918-929, 2010.
[16] T. Y. Lin, S. M. Chen, and M. T. Yu, "Solving the cutting-stock problem by using the Sequential Quadratic Programming optimization method," 2016 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), pp. 1699-1702, 2016.
[17] C. Schmid and L. T. Biegler, "Quadratic programming methods for reduced hessian SQP," Computers & Chemical Engineering, vol. 18, no. 9, pp. 817-832, 1994.