Backstepping-based zero-sum differential games for missile-target interception systems with input and output constraints

In this study, the problem of intercepting a manoeuvring target is posed in a zero-sum differential game problem for a class of strict-feedback non-linear systems with output and input constraints. By introducing a barrier Lyapunov function and an auxiliary system to deal with the output constraints and input constraints, respectively, a novel backstepping feedforward controller is designed to transform the tracking problem for strict-feedback systems into an equivalence differential game problem for affine systems. Subsequently, a zero-sum differential game strategy is developed by using the adaptive dynamic programming technique. A critic network is constructed to learn the Nash equilibrium of the Hamilton-Jacobi-Isaacs equation online. The convergence properties of the proposed backstepping-based differential games are developed by utilising the Lyapunov method. Finally, the effectiveness of the proposed strategy is demonstrated by simulation using missile-target interception system.