## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2013, Special Issue (2013), Article ID 732738, 7 pages.

### Nonlinear ${H}_{\infty }$ Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation

#### Abstract

A conventional region control technique cannot meet the demands for an accurate tracking performance in view of its inability to accommodate highly nonlinear system dynamics, imprecise hydrodynamic coefficients, and external disturbances. In this paper, a robust technique is presented for an Autonomous Underwater Vehicle (AUV) with region tracking function. Within this control scheme, nonlinear ${H}_{\infty }$ and region based control schemes are used. A Lyapunov-like function is presented for stability analysis of the proposed control law. Numerical simulations are presented to demonstrate the performance of the proposed tracking control of the AUV. It is shown that the proposed control law is robust against parameter uncertainties, external disturbances, and nonlinearities and it leads to uniform ultimate boundedness of the region tracking error.

#### Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 732738, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394806115

Digital Object Identifier
doi:10.1155/2013/732738

Mathematical Reviews number (MathSciNet)
MR3124605

Zentralblatt MATH identifier
06950846

#### Citation

Ismail, Zool H.; Dunnigan, Matthew W. Nonlinear ${H}_{\infty }$ Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation. J. Appl. Math. 2013, Special Issue (2013), Article ID 732738, 7 pages. doi:10.1155/2013/732738. https://projecteuclid.org/euclid.jam/1394806115

#### References

• T. Ura, “Autonomous underwater vehicle,” Journal of the Robotics Society of Japan, vol. 18, no. 7, pp. 933–936, 2000 (Japanese).
• D. R. Yoerger and J. E. Slotine, “Robust trajectory control of underwater vehicles,” IEEE Journal of Oceanic Engineering, vol. 10, no. 4, pp. 462–470, 1985.
• R. Cristi, F. A. Papoulias, and A. J. Healey, “Adaptive sliding mode control of autonomous underwater vehicles in the dive plane,” IEEE Journal of Oceanic Engineering, vol. 15, no. 3, pp. 152–160, 1990.
• A. J. Healey and D. Lienard, “Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles,” IEEE Journal of Oceanic Engineering, vol. 18, no. 3, pp. 327–339, 1993.
• J. Guo, F.-C. Chiu, and C.-C. Huang, “Design of a sliding mode fuzzy controller for the guidance and control of an autonomous underwater vehicle,” Ocean Engineering, vol. 30, no. 16, pp. 2137–2155, 2003.
• A. Pisano and E. Usai, “Output-feedback control of an underwater vehicle prototype by higher-order sliding modes,” Automatica, vol. 40, no. 9, pp. 1525–1531, 2004.
• J. J. E. Slotine, “Sliding controller design for nonlinear systems,” International Journal of Control, vol. 40, no. 2, pp. 421–434, 1984.
• J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, New Jersey, NJ, USA, 1991.
• J. Han and K. C. Wan, “Coordinated motion control of underwater vehicle-manipulator system with minimizing restoring moments,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '08), pp. 3158–3163, Nice, France, September 2008.
• J. Han, J. Park, and W. K. Chung, “Robust coordinated motion control of an underwater vehicle-manipulator system with minimizing restoring moments,” Ocean Engineering, vol. 38, no. 10, pp. 1197–1206, 2011.
• Y. Choi and W. K. Chung, PID Trajectory Tracking Control for Mechanical Systems (Lecture Notes in Control and InFormation Sciences), Springer, Berlin, Germany, 2004.
• B. Kim, H. Choi, W. K. Chung, and I. H. Suh, “Analysis and design of robust motion controllers in the unified framework,” ASME Journal of Dynamic Systems, Measurement and Control, vol. 124, no. 2, pp. 313–321, 2002.
• X. Li, S. P. Hou, and C. C. Cheah, “Adaptive region tracking control for autonomous underwater vehicle,” in Proceedings of the 11th International Conference on Control, Automation, Robotics and Vision (ICARCV '10), pp. 2129–2134, Singapore, December 2010.
• Z. H. Ismail, B. M. Mokhar, and M. W. Dunnigan, “Tracking control for an autonomous underwater vehicle based on multiplicative potential energy function,” in Proceedings of the OCEANS 2012 MTS/IEEE Conference, Yeosu, Republic of Korea, 2012.
• Z. H. Ismail, N. Sarman, and M. W. Dunnigan, “Dynamic region boundary-based control scheme for multiple autonomous underwater vehicles,” in Proceedings of the OCEANS 2012 MTS/IEEE Conference, Yeosu, Republic of Korea, 2012.
• T. I. Fossen, Guidance and Control of Ocean Vehicles, John Wiley and Sons, New York, NY, USA, 1st edition, 1994.
• G. Antonelli, Underwater Robots: Motion and Force Control of Vehicle-Manipulator Systems, Springer, Berlin, Germany, 2003.
• J. Park, W. Chung, Y. Youm, and M. Kim, “${H}_{\infty }$ robust motion control of kinematically redundant manipulators,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '98), pp. 330–335, Victoria, Canada, October 1998.
• H. K. Khalil, Nonlinear Systems, Prentice-Hall, Berlin, Germany, 3rd edition, 2001.
• T. K. Podder and N. Sarkar, “Fault-tolerant control of an autonomous underwater vehicle under thruster redundancy,” Robotics and Autonomous Systems, vol. 34, no. 1, pp. 39–52, 2001.
• S. Choi, J. Yuh, and N. Keevil, “design of omni-directional underwater robotic vehicle,” in Proceedings of the Conference on Engineering in Harmony with Ocean (Oceans '93), pp. I192–I197, October 1993.