Closed-loop optimal control based on two-phase pseudospectral convex optimization method for swarm system

The swarm system offers superior flexibility and versatility compared to individual agents. However, to enable the swarm to execute the mission efficiently and cooperatively, it's essential to design an efficient control strategy considering key factors such as computational complexity, speed, and accuracy. This paper summarizes several prominent problems faced by generic swarms, and proposed a two-phase pseudospectral convex optimal closed -loop control method. Firstly, the discrete modalities of cooperative goal, dynamics model, collision avoidance constraint, and control capability constraint are established using the Radau pseudospectral method. Then, these models and constraints are convexified, constructing a pseudospectral convex programming problem model, which can be applied to various types of swarms. To enhance the robustness and computation speed of the control, a two-phase receding horizon method is introduced. In the way, the optimization outcome of the first phase is executed in the subsequent control step, while the simplified second phase will be discarded. The control interval and the initial state of the swarm are continuously updated within the receding horizon until the desired state is reached. Finally, through comprehensive simulation analysis and comparison, the proposed method demonstrates distinct advantages of collision avoidance, optimality, robustness, and high computational efficiency.