Integral Reinforcement Learning for Zero-Sum Games

Two-playerIntegral Reinforcement Learning (IRL) zero-sumReinforcement Learning (RL) gamesTwo-player zero-sum game provideIntegral Reinforcement Learning (IRL) a well-defined framework for addressing \({H_\infty }\) optimal controlOptimal control problems, which have been extensively utilized in designing feedback controllers to mitigate the impact of disturbances on system performance. The exploration of optimal controllers within this framework gained traction following Zames’ contributions (Zames 1981) to the field of optimal controlOptimal control. The solution to such problems can be equated to finding the Nash equilibriumNash equilibrium of the corresponding two-player zero-sum gameTwo-player zero-sum game (Zhang et al. 2011, 2012; Li et al. 2014; Lian et al. 2022), which entails solving the Hamilton–Jacobi–Isaacs (HJIHamilton–Jacobi–Isaacs (HJI)) equation.