Alternate iteration scheme for approximating equilibrium strategy

The two-player differential games is considered to be two mutually coupled optimal control problems (OCPs), and a novel decoupling approach based on Lagrange multipliers is constructed to reformulate the original problem as a non-cooperative game composed of the other two independent OCPs, then a new scheme is proposed to solving these two OCPs alternately and iteratively, and Nash equilibrium of the original problem is approximated progressively. Last by not least, the proposed scheme is used to solve a missile aircraft pursuit-evasion game in a vertical plane, and Gauss pseudospectral method is adopted to solve each OPC, results of simulations not only successfully illustrate the effectiveness of the alternate iteration scheme, process, but also gain a fresh insight into differential game guidance law.