A robust H∞ sampled-data stabilization problem for nonlinear dynamic positioning (DP) ships with Takagi-Sugeno (T-S) fuzzy models is discussed in this paper. Input delay approach is used to convert the sampleddata DP ship system to a fuzzy system with time-varying delay. Adequate conditions are derived to determine the system’s asymptotical stability and achieve H∞ performance via Lyapunov stability theorems. Then, the fuzzy sampled-data controller is obtained by analyzing the stabilization condition. Simulation result shows that the proposed method and the designed controller for a DP ship are effective so that the DP ship can maintain the desired position, heading and velocities in the existence of varying environment disturbances.
ZHENG Minjie (郑敏杰), ZHOU Yujie (周玉洁), YANG Shenhua (杨神化)
. Robust Fuzzy Sampled-Data Control for Dynamic Positioning Ships[J]. Journal of Shanghai Jiaotong University(Science), 2018
, 23(2)
: 209
-217
.
DOI: 10.1007/s12204-018-1931-z
[1] LIU F R, HUI C. Application of moving horizon filterfor dynamic positioning ship [C]//Proceedings of InternationalConference on Computational Intelligenceand Software Engineering. Wuhan, China: IEEE,2010: 1-4. [2] BENETAZZO F, IPPOLITI G, LONGHI S, et al. Dynamicpositioning of a marine vessel using DTVSCand robust control allocation [C]//Proceedings of 20thMediterranean Conference on Control & Automation.Barcelona, Spain: IEEE, 2012: 1211-1216. [3] WITKOWSKA A. Dynamic positioning system withvectorial backstepping controller [C]//Proceedings of18th International Conference on Methods and Modelsin Automation and Robotics. Miedzyzdroje, Poland:IEEE, 2013: 842-847. [4] HASSANI V, S?RENSEN A J, PASCOAL A M, etal. Multiple model adaptive wave filtering for dynamicpositioning of marine vessels [C]//Proceedings of 2012American Control Conference. Montr′eal, Canada:AACC, 2012: 6222-6228. [5] DU J L, HU X, KRSTI′CM, et al. Robust dynamicpositioning of ships with disturbances under input saturation[J]. Automatica, 2016, 73: 207-214 [6] LI H Y, JING X J, LAM H K, et al. Fuzzy sampleddatacontrol for uncertain vehicle suspension systems[J]. IEEE Transactions on Cybernetics, 2014, 44(7):1111-1126. [7] XU L, LIU Z Q. Design of fuzzy PID controller forship dynamic positioning [C]// Proceedings of the 28thChinese Control and Decision Conference. Yichuan,China: IEEE, 2016: 3130-3135. [8] NGONGI W E, DU J L, WANG R. Robust fuzzy controllerdesign for dynamic positioning system of ships[J]. International Journal of Control, Automation andSystems, 2015, 13(5): 1294-1305. [9] HO W H, CHEN S H, CHOU J H. Optimal control ofTakagi-Sugeno fuzzy-model-based systems representingdynamic ship positioning systems [J]. Applied SoftComputing, 2013, 13(7): 3197-3210. [10] SHI P. Filtering on sampled-data systems with parametricuncertainty [J]. IEEE Transactions on AutomaticControl, 1998, 43(7): 1022-1027. [11] FRIDMAN E, SEURET A, RICHARD J P. Robustsampled-data stabilization of linear systems: An inputdelay approach [J]. Automatica, 2004, 40(8): 1441-1446. [12] GAO H J, SUN W C, SHI P. Robust sampled-dataH∞ control for vehicle active suspension systems [J].IEEE Transactions on Control Systems Technology,2010, 18(1): 238-245. [13] WANG Y Y, SHEN H, KARIMI H R, et al.Dissipativity-based fuzzy integral sliding mode controlof continuous-time T-S fuzzy systems [J]. IEEETransactions on Fuzzy Systems, 2017. https://doi.org/10.1109/TFUZZ.2017.2710952 (published online). [14] ZHU X L, CHEN B, YUE D, et al. An improved inputdelay approach to stabilization of fuzzy systems undervariable sampling [J]. IEEE Transactions on FuzzySystems, 2012, 20(2): 330-341. [15] WANG Y Y, XIA Y Q, ZHOU P F. Fuzzy-model-basedsampled-data control of chaotic systems: A fuzzytime-dependent Lyapunov-Krasovskii functional approach[J]. IEEE Transactions on Fuzzy Systems, 2016.https://doi.org/10.1109/TFUZZ.2016.2617378 (publishedonline). [16] WANG Y Y, SHI P. On master-slave synchronizationof chaotic Lur’e systems using sampleddatacontrol [J]. IEEE Transactions on Circuits andSystems II: Express Briefs, 2016. https://doi.org/10.1109/TCSII.2016.2633491 (published online). [17] CHEN W H, WANG Z P, LU X M. On sampled-datacontrol for master-slave synchronization of chaoticLur’e systems [J]. IEEE Transactions on Circuits andSystems II: Express Briefs, 2012, 59(8): 515-519. [18] SHEN B, WANG Z D, LIU X H. Sampled-datasynchronization control of dynamical networks withstochastic sampling [J]. IEEE Transactions on AutomaticControl, 2012, 57(10): 2644-2650. [19] HUA C C, GE C, GUAN X P. Synchronization ofchaotic Lur’e systems with time delays using sampleddatacontrol [J]. IEEE Transactions on Neural Networksand Learning Systems, 2015, 26(6): 1214-1221. [20] WANG Y Y, SHEN H, DUAN D P. On stabilization ofquantized sampled-data neural-network-based controlsystems [J]. IEEE Transactions on Cybernetics, 2017,47(10): 3124-3135. [21] WU Z G, SHI P, SU H Y, et al. Stochastic synchronizationof Markovian jump neural networks with timevaryingdelay using sampled data [J]. IEEE Transactionson Cybernetics, 2013, 43(6): 1796-1806. [22] WU Z G, SHI P, SU H Y, et al. Exponential stabilizationfor sampled-data neural-network-based controlsystems [J]. IEEE Transactions on Neural Networksand Learning Systems, 2014, 25(12): 2180-2190. [23] WANG Y Y, XIA Y Q, SHEN H, et al. SMCdesign for robust stabilization of nonlinear Markovianjump singular systems [J]. IEEE Transactionson Automatic Control, 2017. https://doi.org/10.1109/TAC.2017.2720970 (published online). [24] WANG Y Y, GAO Y B, KARIMI H R, et al. Slidingmode control of fuzzy singularly perturbed systemswith application to electric circuits [J]. IEEE Transactionson System, Man, and Cybernetics: Systems,2017. https://doi.org/10.1109/TSMC.2017.2720968(published online).
