Multi-pursuer single-evader privacy-preserving differential games

This paper investigates a multi-pursuer single-evader (MPSE) differential game with privacy-preserving over time-varying unbalanced directed network topologies. A novel player decomposition mechanism for the MPSE differential game with privacy-preserving is proposed. Distributed control strategies under this mechanism are then designed based on the Hamilton–Jacobi–Isaacs (HJI) and the Nash equilibrium of these strategies is proved. The interception condition related to a proposed novel coupling gain and reconstructed symmetric Laplacian matrix based on the weight balancing method is derived to guarantee that multiple pursuers successfully intercept the evader over time-varying unbalanced directed network topologies. Privacy-preserving is also verified to ensure that the state of any pursuer is not disclosed. Especially, the privacy-preserving algorithm is proved to be applicable to the continuous-time system, which is different from most existing studies whose research system is the discrete-time case. Illustrative examples are given to demonstrate that all pursuers can intercept the evader and that the private information they carry can be preserved.