This article addresses the formation control with obstacle avoidance for a mixed-order linear multi-agent in the ocean environment via a distributed optimal control approach. The considered system is comprised of unmanned aerial vehicles (UAVs), unmanned surface vehicles (USVs) and unmanned underwater vehicles (UUVs). A consensus control law for horizontal direction and height direction is then designed uniformly, and the stability is ensured using block Kronecker product and matrix transformation theory. A linear quadratic regulator method is further designed to achieve distributed optimization. Moreover, for obstacle avoidance in the UUVs, a non-quadratic penalty function is constructed based on the seamount threat model by adopting an inverse optimal control approach. Simulation results confirm the efficiency of the consensus and obstacle avoidance.

本文通过一种分布式最优控制方法解决了海洋环境中混合阶线性多主体的避障编队控制问题。所考虑的系统包括无人飞行器（UAV），无人水面飞行器（USV）和无人水下飞行器（UUV）。然后统一设计了水平方向和高度方向的一致控制律，并使用块Kronecker乘积和矩阵变换理论确保了稳定性。进一步设计了线性二次调节器方法以实现分布式优化。此外，为了避免UUV中的障碍物，采用逆最优控制方法，基于海山威胁模型构造了非二次惩罚函数。