In this paper, the k-valued logic control network is introduced to study the cooperative pursuit control problem of multiple underactuated underwater vehicles (UUVs) with time delay in three-dimensional space. The semi-tensor product of matrices is used to solve the complex calculation problem of the large dimension matrix. The influence of communication delay on multiple UUVs’ optimization and cooperative pursuit control is expressed in a matrix. Under the leadership of evader UUV, the control algorithm can ensure that all the pursuit UUVs reach the desired position. The stability of the closed loop system is proved.

This paper proposes a leader following formation tracking controller for multiple underactuated underwater vehicles (UUVs) which move in three dimensional space. In order to avoid the derivative of the virtual control signals, a control method based on filter backstepping is proposed. The method can significantly simplify the design process of the backstepping controller through the use of a filter rather than the analytic derivation directly to the virtual control variable. Furthermore, the influence of measurement noise is obviously weakened. The stability of the formation system of multiple UUVs has been proved based on Lyapunov stability theory. Simulation results illustrate that the designed controller can track a three-dimensional formation trajectory accurately.

In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with time derivative) and bilinear terms. Applying Coron’s return method, we establish some local controllability results for the position and velocities of the underwater vehicle. Examples with six, four, or only three controls inputs are given for a vehicle with an ellipsoidal shape.