参考文献

[1]柴天佑.工业过程控制系统研究现状与发展方向[J].中国科学：信息科学，2016, 46(8): 1003-1015.

[2]柴天佑.生产制造全流程优化控制对控制与优化理论方法的挑战[J].自动化学报，2009, 35(6): 641-649.

[3]SUN X B, DING J L, WANG H, et al.Iterative learning based particle size distribution control in grinding process using output PDF method[C]//Proceedings of International Conference on Control and Automation, Hangzhou, China, 2013.

[4]ZHANG Y, ZHOUP, LV D, et al.Inverse calculation of burden distribution matrix using B-Spline model based PDF control in blast furnace burden charging process[J].IEEE Transactions on Industrial Informatics, 2023, 19(1):317-327.

[5]LI M J，ZHOUP, LIU Y,et al.Data-driven predictive probability density function control of fiber length stochastic distribution shaping in refining process[J].IEEE Transactions on Automation Science and Engineering, 2020, 17(2):633-645.

[6]ZHANG J F, YUE H, ZHOU J L.Predictive PDF control in shaping of molecular weight distribution based on a new modeling algorithm[J].Journal of Process Control, 2015, 30: 80-89.

[7]ZHU J Y, GUI W H, YANG C H, et al.Probability density function of bubble size based reagent dosage predictive control for copper roughing flotation[J].Control Engineering Practice, 2014, 29(8): 1-12.

[8]WANG H.Bounded dynamic stochastic distributions modelling and control[M].London: Springer-Verlag, 2000.

[9]KÁRNÝ M.Towards fully probabilistic control design[J].Automatica, 1996, 32(12): 1719-1722.

[10]FORBES M G, FORBES J F, GUAY M.Regulatory control design for stochastic processes: shaping the probability density function[C]//Proceedings of the 2003 American Control Conference, Denver, USA, 2003.

[11]FORBES M G, GUAY M.Nonlinear stochastic control via stationary response design[J].Probabilistic Engineering Mechanics, 2003, 18(1): 79-86.

[12]FORBES M G, GUAY M, FORBES J E.Control design for first-order processes: shaping the probability density of the process state[J].Journal of Process Control, 2004, 14(4): 399-410.

[13]ELBEYLI O, HONG L, SUN J Q.On the feedback control of stochastic systems tracking pre-specified probability density functions[J].Transactions of the Institute of Measurement and Control, 2005, 27(5): 319-330.

[14]JONES D G, WANG H.A new non-linear optimal control strategy for paper formation[J].Institute of Measurement and Control, 1999, 32(8): 241-245.

[15]WANG H.Detect unexpected changes of particle size distribution in paper-making white water systems[C]//Proceedings of the 3rd IFAC Workshop on on-line Fault Detection and Supervision in the Chemical Process Industry, Lyon, France, 1998.

[16]YUE H, JIAO J, BROWN E L, et al.Real-time entropy control of stochastic systems for an improved paper web formation[J].Measure & Control, 2001, 34(5):134-139.

[17]NOBAKHTI A, WANG H.Minimization of wet end disturbances during web breaks using online LAV estimation[J].Control Engineering Practice, 2010, 18(4): 433-447.

[18]岳红，王宏，张金芳.聚合物生产分子量分布建模与控制研究[J].化工自动化及仪表，2004, 31(6):1-7.

[19]REN Y W, WANG A P, WANG H.Fault diagnosis and tolerant control for discrete stochastic distribution collaborative control systems[J].IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2015, 45(3): 462-471.

[20]申珊华，曹柳林，王晶.基于分布函数矩的聚合物分子量分布预测控制[J].化工学报，2013, 64(12): 4379-4384.

[21]WANG H.Control of the output probability density functions for a class of nonlinear stochastic systems[C]//Proceedings IFAC Workshop on Algorithms & Architecture for Real Time Control, Cancun, Mexico, 1998.

[22]WANG H.Control for bounded pseudo ARMAX stochastic systems via linear B-Spline approximations[C]//Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000.

[23]WANG H.Robust control of the output probability density functions for multivariable stochastic systems with guaranteed stability[J].IEEE Transactions on Automatic Control, 1999, 41(11): 2103-2107.

[24]WANG H, ZHANG J H.Bounded stochastic distribution control for pseudo ARMAX systems[J].IEEE Transactions on Automatic Control, 2001, 46(3): 486-490.

[25]WANG H.Minimum entropy control for non-Gaussian dynamic stochastic systems[J].IEEE Transactions on Automatic Control, 2002, 47(2): 398-403.

[26]WANG A P, AFSHAR P, WANG H.Complex stochastic system modeling and control via iterative machine learning[J].Neurocomputing, 2008, 71(13-15): 2685-2692.

[27]WANG H, AFSHAR P.ILC-based fixed-structure controller design for output PDF shaping in stochastic systems using LMI technique[J].IEEE Transactions on Automatic Control, 2009, 54(4): 760-773.

[28]ZHOU J L, YUE H, ZHANG J F, et al.Iterative learning double closed-loop structure for modeling and controller design of output stochastic distribution control systems[J].IEEE Transactions on Control Systems Technology, 2014, 22(6): 2261-2276.

[29]AFSHAR P.Intelligent model reference adaptive distribution control for non- Gaussian stochastic systems[C]//Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, Okayama, Japan, 2009.

[30]ZHOU J L, WANG X, ZHANG J F, et al.A new measure of uncertainty and the control loop performance assessment for output stochastic distribution systems[J].IEEE Transactions on Automatic Control, 2015, 60(9): 2524-2529.

[31]YUE H, ZHOU J L, WANG H.Minimum entropy of B-spline PDF systems with mean constraint[J].Automatica, 2006, 42(6): 989-994.

[32]WANG Y J, WANG H.Suboptimal mean controllers for bounded and dynamic stochastic distributions[J].Journal of Process Control, 2002, 12(3): 1281-1288.

[33]ZHOU J L, LI G T, WANG H.Robust tracking controller design for non-Gaussian singular uncertainty stochastic distribution systems[J].Automatica, 2014, 50(4): 1296-1303.

[34]陈海永，王宏.基于LMI的参数随机变化系统的概率密度函数控制[J].自动化学报，2007, 33(11): 1216-1220.

[35]周靖林，王宏.输出概率密度函数的最优跟踪控制：均方根B样条模型[J].控制理论与应用，2005, 22(3): 369-376.

[36]王宏，岳红.随机系统输出分布的建模、控制与应用[J].控制工程，2003, 10(3): 3-7.

[37]ZHOU J L, YUE H, WANG H.Shaping of output PDF based on the rational square-root B-Spline Model[J].Acta Automatica Sinica, 2005, 31(3): 343-351.

[38]姚利娜，王宏.基于有理平方根逼近的非高斯随机分布系统的故障诊断和容错控制[J].控制理论与应用，2006, 23(4): 562-568.

[39]ZHOU P, LI M J, GUO D W, et al.Modeling for output fiber length distribution of refining process using wavelet neural networks trained by NSGA-Ⅱ and gradient based two-stage hybrid algorithm[J].Neurocomputing, 2017, 238(C): 24-32.

[40]王宏，丁进良，柴天佑，等.随机分布控制系统研究进展及应用[C]//2009年中国自动化大会暨两化融合高峰会议，杭州，中国，2010.

[41]GUO L, WANG H.PID controller design for output PDFs of stochastic systems using linear matrix inequalities[J].IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2005, 35(1): 65-71.

[42]GUO L, WANG H.Generalized discrete-time PI control of output PDFs using square root B-spline expansion[J].Automatica, 2005, 41(1): 159-162.

[43]YI Y, GUO L, WANG H.Constrained PI tracking control for output probability distributions based on two-step neural networks[J].IEEE Transactions on Circuits and Systems-I, 2009, 56(7): 1416-1426.

[44]WANG H, ZHANG J F, YUE H.Multi-step predictive control of a PDF shaping problem[J].Acta Automatica Sinica, 2005, 31(2): 274-279.

[45]WANG H.Model reference adaptive control of the output stochastic distributions for unknown linear stochastic systems[J].International Journal of Systems Science, 1999, 30(7): 707-719.

[46]YI Y, GUO L, WANG H.Adaptive statistic tracking control based on two steps neural networks with time delays[J].IEEE Transactions on Neural Networks, 2009, 20(3): 420-429.

[47]LI G, ZHAO Q.Adaptive Fault-tolerant stochastic shape control with application to particle distribution control[J].IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2015, 45(12): 1592-1604.

[48]LIU Y, WANG H, HOU C H.Sliding-mode control design for nonlinear systems using probability density function shaping[J].IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(2): 332-343.

[49]ARIMOTO S, KAWAMURA S, MIYAZAKI F.Bettering operation of robots by learning[J].Journal of Robotic Systems, 1984, 1(2): 123-140.

[50]ARIMOTO S, KAWAMURA S, MIYAZAKI F.Bettering operation of dynamic systems by learning: A new control theory for servomechanism or mechatronic system[C]//Processing of the 23rd Conference on Decision and Control, Las Vegas, NV, USA, 1984.

[51]WANG Y Q, GAO F R, DOYLE F J.Survey on iterative learning control, repetitive control, and run-to-run control[J].Journal of Process Control, 2009, 19(10): 1589-1600.

[52]CHI R H, LIU X H, ZHANG R K, et al.Constrained data-driven optimal iterative learning control[J].Journal of Process Control, 2017, 55: 10-29.

[53]JANSSENS P, PIPELEERS G, SWEVERS J.A data-driven constrained norm-optimal iterative learning control framework for LTI systems[J].IEEE Transactions on Control Systems Technology, 2013, 21(2): 546-551.

[54]ZHOU J L, ZHOU D H, WANG H, et al.Distribution function tracking filter design using hybrid characteristic functions[J].Automatica, 2010, 46(1): 101-109.

[55]GUO L, YIN L P, WANG H, et al.Entropy optimization filtering for fault isolation of nonlinear non-Gaussian stochastic systems[J].IEEE Transactions on Automatic Control, 2009, 54(4): 804-810.

[56]GUO L, WANG H, CHAI T Y.Fault detection for non-linear non-Gaussian stochastic systems using entropy optimization principle[J].Transactions of the Institute of Measurement and Control, 2006, 28(2): 145-161.

[57]YAO L N, QIN J F, WANG H, et al.Design of new fault diagnosis and fault tolerant control scheme for non-Gaussian singular stochastic distribution systems[J].Automatica, 2012, 48(9): 2305-2313.

[58]YIN L P, GUO L.Fault isolation for dynamic multivariate nonlinear non-Gaussian stochastic systems using generalized entropy optimization principle[J].Automatica, 2009, 45(11): 2612-2619.

[59]YAO L N, PENG B.Fault diagnosis and fault tolerant control for the non-Gaussian time-delayed stochastic distribution control system[J].Journal of the Franklin Institute, 2014, 351(3): 1577-1595.

[60]YI L P, GUO L.Robust PDF control with guaranteed stabilityfor non-linear stochastic systems undermodelling errors[J].IET Control Theory & Applications, 2009, 3(5): 575-582.

[61]孙绪彬.输出PDF建模与控制及其在火焰温度场中的应用[D].北京：中国科学院研究生院，2007.

[62]张金芳，赵建勋，李进.随机分布控制在炉膛截面温度场中的应用研究[J].计算机与现代化，2017, 5: 45-49.

[63]彭建恩.制粉工艺与设备[M].成都：西南交通大学出版社，2005.

[64]李林轩，王晓芳，李硕.小麦制粉工艺控制与设备操作管理[J].粮食加工，2012, 37(6): 14-17.

[65]ZHU J Y, GUI W H, LIU J P, et al.Combined fuzzy based feed forward and bubble size distribution based feedback control for reagent dosage in copper roughing process[J].Journal of Process Control, 2016, 39: 50-63.

[66]XIE Y F, CAO B F, HE Y P, et al.Reagent dosages control based on bubble size characteristics for flotation process[J].IET Control Theory & Applications, 2016, 10(12): 1404-1411.

[67]ZHU J Y, GUI W H, YANG C H, et al.Probability density function of bubble size based reagent dosage control for flotation process[J].Asian Journal of Control, 2014, 16(3): 765-777.

[68]朱建勇，桂卫华，阳春华，等.基于泡沫尺寸随机分布的铜粗选药剂量控制[J].自动化学报，2014, 40(10): 2089-2097.

[69]刘金平，桂卫华，唐朝晖，等.基于泡沫大小动态分布的浮选生产过程加药量健康状态分析[J].控制理论与应用，2013, 30(4): 492-502.

[70]BARATTI R, TRONCI S, ROMAGNOLI J A.A generalized stochastic modelling approach for crystal size distribution in antisolvent crystallization operations[J].AIChE Journal, 2017, 63(2): 551-559.

[71]GHADIPASHA N, ROMAGNOLI J A, TRONCI S, et al.A model-based approach for controlling particle size distribution in combined cooling-antsolvent crystallization processes[J].Chemical Engineering Science, 2018, 23(190): 260-272.

[72]陈海永.随机分布控制及其在焊缝跟踪系统中的可行性研究[D].北京：中国科学院研究生院，2008. Y4StbmgbqWH5w4uIUtYKV799pEGSiTbUk2pPXrgpxAQ5k0EDBStyjba45SoPLWoZ