Journal of Systems Engineering and Electronics ›› 2020, Vol. 31 ›› Issue (4): 780-791.doi: 10.23919/JSEE.2020.000053

• Control Theory and Application • Previous Articles     Next Articles

Adaptive back-stepping control on container ships for path following

Yang ZHAO1(), Lili DONG2,*()   

  1. 1 Physics and Engineering Department, Taylor University, Upland IN 46989, USA
    2 Department of Electrical Engineering and Computer Science, Cleveland State University, Cleveland OH 44115, USA
  • Received:2019-07-15 Online:2020-08-25 Published:2020-08-25
  • Contact: Lili DONG;
  • About author:ZHAO Yang was born in 1986. He received his Ph.D. degree in electrical engineering from Cleveland State University, Cleveland, OH, USA, in 2019. He completed his M.S. degree in electrical engineering from Cleveland State University, Cleveland, OH, USA, in 2013. He is an assistant professor in the Physics and Engineering Department at Taylor University. He is an IEEE-HKN member, and he served as the president of the HKN Honor Society, Epsilon Alpha Chapter, in 2016. His research interests include the robust speed control of permanent magnet synchronous motors, the path-following control of under-actuated ships, and the disturbance rejection control of power systems. E-mail: yang|DONG Lili was born in 1974. She received her Ph.D. degree in electrical engineering from University of Alabama, Tuscaloosa, AL, USA, in 2005. She is an associate professor in the Department of Electrical Engineering and Computer Science at Cleveland State University, Cleveland, OH, USA. She is the chair of the IEEE Control Systems Society, Cleveland Chapter. Her current research interests include control systems design and implementations, and control applications to power systems, automobiles, marine ships, and micro-electromechanical systems (MEMS). She is an editor for the Proceedings of American Control Conference and an associate editor of ISA Transactions. E-mail:


A feedback-dominance based adaptive back-stepping (FDBAB) controller is designed to drive a container ship to follow a predefined path. In reality, current, wave and wind act on the ship and produce unwanted disturbances to the ship control system. The FDBAB controller has to compensate for such disturbances and steer the ship to track the predefined (or desired) path. The difference between the actual and the desired path along which the ship is to sail is defined as the tracking error. The FDBAB controller is built on the tracking error model which is developed based on Serret-Frenet frame transformation (SFFT). In additional to being affected by external disturbances, the ship has more outputs than inputs (under-actuated), and is inherently nonlinear. The back-stepping controller in FDBAB is used to compensate the nonlinearity. The adaptive algorithms in FDBAB is employed to approximate disturbances. Lyapunov's direct method is used to prove the stability of the control system. The FDBAB controlled system is implemented in Matlab/Simulink. The simulation results verify the effectiveness of the controller in terms of successful path tracking and disturbance rejection.

Key words: under-actuated, nonlinear, environmental disturbance, path following, Serret-Frenet frame transformation (SFFT), ship steering