H∞ control of linear discrete-time systems: Off-policy reinforcement learning

In this paper, a model-free solution to the H∞ control of linear discrete-time systems is presented. The proposed approach employs off-policy reinforcement learning (RL) to solve the game algebraic Riccati equation online using measured data along the system trajectories. Like existing model-free RL algorithms, no knowledge of the system dynamics is required. However, the proposed method has two main advantages. First, the disturbance input does not need to be adjusted in a specific manner. This makes it more practical as the disturbance cannot be specified in most real-world applications. Second, there is no bias as a result of adding a probing noise to the control input to maintain persistence of excitation (PE) condition. Consequently, the convergence of the proposed algorithm is not affected by probing noise. An example of the H∞ control for an F-16 aircraft is given. It is seen that the convergence of the new off-policy RL algorithm is insensitive to probing noise.