# Design of Adaptive Neural Tracking Controller for Pod Propulsion Unmanned Vessel Subject to Unknown Dynamics

• Mu, Dong-Dong (School of Information Science and Technology, Dalian Maritime University) ;
• Wang, Guo-Feng (School of Information Science and Technology, Dalian Maritime University) ;
• Fan, Yun-Sheng (School of Information Science and Technology, Dalian Maritime University)
• Received : 2017.03.25
• Accepted : 2017.07.06
• Published : 2017.11.01
• 33 6

#### Abstract

This paper addresses two interrelated problems concerning the tracking control of pod propulsion unmanned surface vessel (USV), namely, the modeling of pod propulsion USV, and tracking controller design. First, based on MMG modeling theory, the model of pod propulsion USV is derived. Furthermore, a practical adaptive neural tracking controller is proposed by backstepping technique, neural network approximation and adaptive method. Meanwhile, unlike some existing tracking methods for surface vessel whose control algorithms suffer from "explosion of complexity", a novel neural shunting model is introduced to solve the problem. Using a Lyapunov functional, it is proven that all error signals in the system are uniformly ultimately bounded. The advantages of the paper are that first, the underactuated characteristic of pod propulsion USV is proved; second, the neural shunting model is used to solve the problem of "explosion of complexity", and this is a combination of knowledge in the field of biology and engineering; third, the developed controller is able to capture the uncertainties without the exact information of hydrodynamic damping structure and the sea disturbances. Numerical examples have been given to illustrate the performance and effectiveness of the proposed scheme.

#### Keywords

Pod;USV;Modeling;Tracking control;Adaptive;Robot and automation

#### Acknowledgement

Supported by : Nature Science Foundation of Liaoning Province of China, Nature Science Foundation of China, Central Universities

#### References

1. Sinisterra A J, Dhanak M R and Ellenrieder K V, "Stereovision-based target tracking system for USV operations," Ocean Engineering, vol. 133, pp. 197-214, Feb. 2017. https://doi.org/10.1016/j.oceaneng.2017.01.024
2. Song S H, Yoon Y H, Lee B K and Won C Y, "Autonomous Underwater Vehicles with Modeling and Analysis of 7-Phase BLDC Motor Drives," Journal of Electrical Engineering & Technology, vol. 9, no. 9, pp. 932-941, Sep. 2014. https://doi.org/10.5370/JEET.2014.9.3.932
3. Mu D, Wang G, Fan Y and Zhao Y, "Modeling and Identification of Podded Propulsion Unmanned Surface Vehicle and Its Course Control Research," Mathematical Problems in Engineering, no. 4, pp. 1-13, Apr. 2017.
4. Sonnenburg C R and Woolsey C A, "Modeling, Identification, and Control of an Unmanned Surface Vehicle," Journal of Field Robotics, vol. 30, no. 3, pp. 371-398, Mar. 2013. https://doi.org/10.1002/rob.21452
5. Jiang Z P, "Global tracking control of underactuated ships by Lyapunov's direct method," Automatica, vol. 38, no. 2, pp. 301-309, Feb. 2002. https://doi.org/10.1016/S0005-1098(01)00199-6
6. Do K D, Jiang Z P and Pan J, "Robust global stabilization of underactuated ships on a linear course: State and output feedback," American Control Conference, 2002. Proceedings of the IEEE, Anchorage, USA, Nov 2002.
7. Do K D, Jiang Z P and Pan J, "Underactuated ship global tracking under relaxed conditions," IEEE Transactions on Automatic Control, vol. 47, no. 9. pp. 1529-1536, Sep. 2002. https://doi.org/10.1109/TAC.2002.802755
8. Ma B, "Global $\kappa$-exponential asymptotic stabilization of underactuated surface vessels," Systems & Control Letters, vol. 58, no. 3, pp. 194-201, Mar. 2009. https://doi.org/10.1016/j.sysconle.2008.10.011
9. Liao Y L, Wan L and Zhuang J Y, "Backstepping Dynamical Sliding Mode Control Method for the Path Following of the Underactuated Surface Vessel," Procedia Engineering, vol. 15, no. 7, pp. 256-263, Aug. 2011. https://doi.org/10.1016/j.proeng.2011.08.051
10. Yang Y, Du J, Liu H, Guo C and Abraham A, "A Trajectory Tracking Robust Controller of Surface Vessels With Disturbance Uncertainties," IEEE Transactions on Control Systems Technology, vol. 22, no. 4, pp. 1511-1518, Jul. 2014. https://doi.org/10.1109/TCST.2013.2281936
11. Zhang G, Zhang X and Zheng Y, "Adaptive neural path-following control for underactuated ships in fields of marine practice," Ocean Engineering, vol. 104, pp. 558-567, Jun. 2015. https://doi.org/10.1016/j.oceaneng.2015.05.013
12. Liu L, Wang D and Peng Z, "Path following of marine surface vehicles with dynamical uncertainty and time-varying ocean disturbances," Neurocomputing, vol.173, pp.799-808, Aug. 2016. https://doi.org/10.1016/j.neucom.2015.08.033
13. Peng Z, Wang D and Hu X, "Robust adaptive formation control of underactuated autonomous surface vehicles with uncertain dynamics," Iet Control Theory & Applications, vol. 5, no. 12, pp. 1378-1387, Aug. 2011. https://doi.org/10.1049/iet-cta.2010.0429
14. Tian Z, Li S, Wang Y and Wang X, "A Network Traffic Hybrid Prediction Model Optimized by Improved Harmony Search Algorithm," Neural Network World, vol.25, no.6, pp.669-685, Jun. 2015. https://doi.org/10.14311/NNW.2015.25.034
15. Park B S, Kwon J W and Kim H, "Neural networkbased output feedback control for reference tracking of underactuated surface vessels," Automatica, vol. 77, pp. 353-359, Jan. 2017. https://doi.org/10.1016/j.automatica.2016.11.024
16. Chang W, Tong S and Li Y, "Adaptive fuzzy Backstepping output constraint control of flexible manipulator with actuator saturation," Neural Computing & Applications, pp.1-11, Jun. 2016.
17. Tian Z, Li S and Wang Y, "TS fuzzy neural network predictive control for burning zone temperature in rotary kiln with improved hierarchical genetic algorithm," International Journal of Modelling, Identification and Control, vol. 25, no. 4, pp. 323-334, Jul. 2016.
18. Tian Z, Gao X and Wang D, "The Application Research of Fuzzy Control with Self-tuning of Scaling Factor in the Energy Saving Control System of Pumping Unit," Engineering Letters, vol. 24. no. 2, pp. 187-194, Feb. 2016.
19. Tian Z, Li S, Wang Y and Zhang Q, "Multi Permanent Magnet Synchronous Motor Synchronization Control based on Variable Universe Fuzzy PI Method," Engineering Letters, vol. 23, no. 3. pp. 180-188, Mar. 2015.
20. Pan C Z, Lai X Z, Yang S X and Wu M, "An efficient neural network approach to tracking control of an autonomous surface vehicle with unknown dynamics," Expert Systems with Applications, vol. 40, no. 5, pp. 1629-1635, Apr. 2013. https://doi.org/10.1016/j.eswa.2012.09.008
21. Abbas H A, Belkheiri M and Zegnini B, "Feedback Linearization Control for Highly Uncertain Nonlinear Systems Augmented by Single-Hidden-Layer Neural Networks," Journal of Engineering Science & Technology Review, vol.8, no.2, pp.215-224, Feb. 2015.
22. Do K D, "Practical control of underactuated ships," Ocean Engineering, vol. 37, no. 13, pp. 1111-1119, Sep. 2010. https://doi.org/10.1016/j.oceaneng.2010.04.007
23. Krstic M, Kokotovic P V and Kanellakopoulos I, Nonlinear and Adaptive Control Design: John Wiley & Sons, Inc. 1995.
24. Yang Y S and Wang X F, "Adaptive $H_{\infty}$ tracking control for a class of uncertain nonlinear systems using radial-basis-function neural networks," Neurocomputing, vol. 70, no. 4, pp. 932-941, Jan. 2007. https://doi.org/10.1016/j.neucom.2006.10.020
25. Li J H, Lee P M, Jun B H and Lim Y K, "Point-topoint navigation of underactuated ships," Automatica, vol. 44, no. 12, pp. 3201-3205, Nov. 2008. https://doi.org/10.1016/j.automatica.2008.08.003
26. Yang S X and Meng M, "An efficient neural network approach to dynamic robot motion planning," Neural Networks, vol. 13, no. 2, pp. 143-148, Mar. 2000. https://doi.org/10.1016/S0893-6080(99)00103-3
27. Du J, Hu X, Krstic M and Sun Y, "Robust dynamic positioning of ships with disturbances under input saturation," Automatica, vol. 73, pp. 207-214, Nov. 2016. https://doi.org/10.1016/j.automatica.2016.06.020
28. Zeng B, "Research on Nonlinear Control of Waterjet Propulsion Surface Unmanned Naval vessel," Harbin Engineering University, 2012.
29. Do K D and Pan J, "Robust adaptive path following of underactuated ships," Automatica, vol. 40, no. 6, pp. 929-944, Jun, 2004. https://doi.org/10.1016/j.automatica.2004.01.021
30. Li T S, Wang D, Feng G and Tong S C, "A DSC Approach to Robust Adaptive NN Tracking Control for Strict-Feedback Nonlinear Systems," IEEE Transactions on Systems Man & Cybernetics Part B, vol. 40, no. 3, pp. 915-927, Jun. 2010. https://doi.org/10.1109/TSMCB.2009.2033563
31. Chwa D, "Global Tracking Control of Underactuated Ships With Input and Velocity Constraints Using Dynamic Surface Control Method," IEEE Transactions on Control Systems Technology, vol. 19, no. 6, pp. 1357-1370, Nov. 2011. https://doi.org/10.1109/TCST.2010.2090526
32. Do K D and Pan J, Control of ships and underwater vehicles: design for underactuated and nonlinear marine systems: Springer, 2009.
33. Tee K P and Ge S S, "Control of fully actuated ocean surface vessels using a class of feed-forward approximators," IEEE Transactions on Control Systems Technology, vol. 14, no. 4, pp. 750-756, Jul. 2006. https://doi.org/10.1109/TCST.2006.872507
34. Dai S L, Wang C and Luo F, "Identification and learning control of ocean surface ship using neural networks," IEEE Transactions on Industrial Informatics, vol. 8, no. 4, pp. 801-810, Nov. 2012. https://doi.org/10.1109/TII.2012.2205584
35. Fossen T I, Marine Control Systems: Guidance, Navigation, and Control of Ships rigs and underwater vehicles: Marine Cybernetics, 2002.
36. Du J L, Guo C and Yang C E, "Adaptive Nonlinear Design of autopilot for Ship Course Tracking," Journal of Applied Science, vol.24, no.1, pp.83-88, Jan. 2006.