Model-Free Linear Discrete-Time System H∞ Control Using Input-Output Data

In this paper, a data-driven output feedback H
_∞
control algorithm for discrete-time linear systems with unknown dynamics has been proposed. At first, the standard model-based state feedback H
_∞
controller is formulated. Then, considering the state is not measurable and the system dynamic is unknown for some systems, we reformulate the value function of the H
_∞
control problem based on historical input and output data. Using the novel value function and adaptive dynamic programming approach, an online data-driven output feedback H
_∞
control algorithm for linear discrete-time systems is proposed. Different from on-policy reinforcement learning based model-free control algorithms, the proposed algorithm can eliminate the influence of probing noise to guarantee unbiased solutions. A simulation example is employed to verify the effectiveness of the proposed control algorithm.