Leader–follower formation source seeking control of multiple ships using sliding mode active disturbance rejection observer

In this paper, the control of multiple ships for unknown scalar field source seeking problem with unknown external disturbances is considered. The sliding mode active disturbance rejection observers are designed first to converge to fixed multiple of the unknown external disturbances in finite time, respectively, and a least square method is adopted to estimate the gradient of the unknown scalar field at the position of the leading ship. Second, the surge, sway and angle velocity of the leading ship can converge to the virtual kinematic controllers through the input control of the dynamic controllers using force and torque in finite time. Third, the virtual controllers and dynamic controllers of the following ships are developed to urge the following ships to accomplish the source seeking problem from the perspective of dynamics. Finally, theoretical proofs and simulations are provided to prove the effectiveness of the strategy proposed.