Coordinated control for multiple underactuated underwater vehicles with time delay in game theory frame

The coordinated control for multiple underactuated underwater vehicles (UUVs) is studied in this paper. Firstly, the control problem is formulated under the mix-valued logic control networks in game theory frame. The desired position of the i-th follower UUV is selected by the leader UUV and the other follower UUV's strategies. Secondly, the semi-tensor product (STP) of matrices is used in this paper. The STP of matrices extends the traditional matrix multiplication to two arbitrary dimension matrix multiplication so as to solve the complicated calculation of big data. Finally, the time delay is considered in the coordinated dynamics. The logic matrix with time delay is proposed in the optimal coordinated control. The optimal control strategy is deduced from the algebraic structure in game theory frame. At the same time, the control force and moment are derived.