  In this paper, we propose a model-free adaptive learning solution for a
model-following control problem. This approach employs policy iteration, to
find an optimal adaptive control solution. It utilizes a moving finite-horizon
of model-following error measurements. In addition, the control strategy is
designed by using a projection mechanism that employs Lagrange dynamics. It
allows for real-time tuning of derived actor-critic structures to find the
optimal model-following strategy and sustain optimized adaptation performance.
Finally, the efficacy of the proposed framework is emphasized through a
comparison with sliding mode and high-order model-free adaptive control
approaches. Keywords: Model Reference Adaptive Systems, Reinforcement Learning,
adaptive critics, control system, stochastic, nonlinear system
