  Reinforcement learning (RL) is a class of artificial intelligence algorithms
being used to design adaptive optimal controllers through online learning. This
paper presents a model-free, real-time, data-efficient Q-learning-based
algorithm to solve the H$_{\infty}$ control of linear discrete-time systems.
The computational complexity is shown to reduce from
$\mathcal{O}(\underline{q}^3)$ in the literature to
$\mathcal{O}(\underline{q}^2)$ in the proposed algorithm, where $\underline{q}$
is quadratic in the sum of the size of state variables, control inputs, and
disturbance. An adaptive optimal controller is designed and the parameters of
the action and critic networks are learned online without the knowledge of the
system dynamics, making the proposed algorithm completely model-free. Also, a
sufficient probing noise is only needed in the first iteration and does not
affect the proposed algorithm. With no need for an initial stabilizing policy,
the algorithm converges to the closed-form solution obtained by solving the
Riccati equation. A simulation study is performed by applying the proposed
algorithm to real-time control of an autonomous mobility-on-demand (AMoD)
system for a real-world case study to evaluate the effectiveness of the
proposed algorithm.
