  The stochastic $H_{\infty}$ control is studied for a linear stochastic It\^o
system with an unknown system model. The linear stochastic $H_{\infty}$ control
issue is known to be transformable into the problem of solving a so-called
generalized algebraic Riccati equation (GARE), which is a nonlinear equation
that is typically difficult to solve analytically. Worse, model-based
techniques cannot be utilized to approximately solve a GARE when an accurate
system model is unavailable or prohibitively expensive to construct in reality.
To address these issues, an off-policy reinforcement learning (RL) approach is
presented to learn the solution of a GARE from real system data rather than a
system model; its convergence is demonstrated, and the robustness of RL to
errors in the learning process is investigated. In the off-policy RL approach,
the system data may be created with behavior policies rather than the target
policies, which is highly significant and promising for use in actual systems.
Finally, the proposed off-policy RL approach is validated on a stochastic
linear F-16 aircraft system.
