This paper studies the problem of target control and how a virtual ellipsoid can avoid the static obstacle. During the motion to the target set, the virtual ellipsoid can achieve a motion under collision avoidance by keeping the distance between the ellipsoid and obstacle. We present solutions to this problem in the class of closed-loop (feedback) controls based on Hamilton–Jacobi–Bellman (HJB) equation. Simulation results verify the validity and effectiveness of our algorithm.

There is tremendous interest in designing feedback strategy control for clusters in modern control theory. We propose a novel numerical solution to target team control problems by using the Hamilton formalism methods. In order to ensure the smooth wireless information exchange, all members of the team are located in a virtual ellipsoidal container during the whole movement process. An ellipsoidal container tube is constructed as the external state constraint of the team. The corresponding value function is then formulated based on collision avoidance conditions and energy constraints in the process of the team motion. Time-dependent partial differential equations are formulated based on Hamilton formalism, which have been solved numerically by using the traditional finite difference method (FDM). The objective of the presented method is to obtain optimal control and motion trajectory of the cluster at each moment. Lastly, we conduct a simulation study of unmanned aerial vehicles (UAVs) to demonstrate the performance of the proposed method.