ISS-based robust adaptive fuzzy algorithm for maintaining a ship’s track

Abstract

This paper focuses on the problem of linear track keeping for marine surface vessels. The influence exerted by sea currents on the kinematic equation of ships is considered first. The input-to-state stability (ISS) theory used to verify the system is input-to-state stable. Combining the Nussbaum gain with backstepping techniques, a robust adaptive fuzzy algorithm is presented by employing fuzzy systems as an approximator for unknown nonlinearities in the system. It is proved that the proposed algorithm that guarantees all signals in the closed-loop system are ultimately bounded. Consequently, a ship’s linear track-keeping control can be implemented. Simulation results using Dalian Maritime University’s ocean-going training ship ‘YULONG’ are presented to validate the effectiveness of the proposed algorithm.

Keywords

ISS theory / adaptive control / fuzzy system / ship track-keeping

References

[1] Fossen T. I. Recent developments in ship control systems design[M]. 2000, London: Sterling Publications Limited

[2] ZHANG R, CHEN Y B, SUN Z Q, et al. Path control of a surface ship in restricted waters using sliding mode[A]. Proc of the 37th IEEE CDC[C]. Tampa, 1998.

[3] ENCARNACAO P, PACOAL A, ARCAK M. Path following for autonomous marine craft[A]. Proc of the 5th IFAC Conf on MCMC[C]. Aalborg, Denmark, 2000.

[4] INDIVERI G, AICARDI M, CASALINO G. Nonlinear time-invariant feedback control of an underactuated marine vehicle along a straight course[A]. Proc of the IFAC Conference on Manoeuvring and Control of Marine Craft[C]. Aalborg, Denmark, 2000.

[5] PETTERSEN K Y, LEFEBER E. Way-point tracking control of ships[A]. Proceedings of the 40th IEEE CDC[C]. Orlando, USA, 2001.

[6] DO K D, JIANG Z P, PAN J. Robust global stabilization of underactuated ships on a linear course: state and output feedback[J]. Int J Control, 2003, (76)1: 1–17.

[7] Li T. S., Yang Y. S. Nonlinear control of underactuated ships[J]. Journal of Traffic and Transportation Engineering, 2003, 3(4): 39-43

[8] LI T S, YANG Y S, HONG B, et al. A robust adaptive nonlinear control approach to ship straight-path tracking design[A]. Proceedings of the 2005 American Control Conference[C]. Portland, USA, 2005.

[9] BREIVIK M, FOSSEN T I. Path Following of straight lines and circles for marine surface vessels[A]. Proc of the IFAC CAMS’04[C]. Ancona, Italy, 2004.

[10] Nussbaum R. D. Some remarks on the conjecture in parameter adaptive control[J]. System and Control Letters, 1983, 3(11): 243-246

[11] Ge S. S., Wang J. Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems[J]. IEEE Trans on Neural Networks, 2002, 13(6): 1409-1419

[12] Ryan E. P. A universal adaptive stabilizer for a class of nonlinear systems[J]. System and Control Letters, 1991, 16: 209-218

[13] Wang L. X. Adaptive fuzzy systems and control-design and stability analysis[M]. 1994, New Jersey: Prentice Hall

[14] Sontag E. D. Further results about input-state stabilization[J]. IEEE Trans on Automatic Control, 1990, 35: 473-476