Abstract
In this paper, cooperative control and optimal control methods are used for the formation control of mixed-order heterogeneous multi-agent systems. The system consists of unmanned aerial vehicles (UAVs), unmanned surface vehicles (USVs), and unmanned underwater vehicles (UUVs). The system is represented in a state space using a block Kronecker product. The static and dynamic formation control protocols are proposed respectively, and the graph theory is used to prove that formation control protocols can realize system formation. Furthermore, the optimal control and cooperative control are introduced into the static and the dynamic formation control protocols, and the static cooperative optimal formation control protocol and the dynamic cooperative optimal formation control protocol are designed. Through MATLAB simulation, the static cooperative optimal control protocol and static formation control protocol are compared, and the dynamic cooperative optimal control protocol and dynamic formation control protocol are compared. By comparison, the state variables of the system can reach convergence quickly, and the system can complete formation in a short time, which verifies the effectiveness of the optimal theory and cooperative control.