  In this paper, a novel online, output-feedback, critic-only, model-based
reinforcement learning framework is developed for safety-critical control
systems operating in complex environments. The developed framework ensures
system stability and safety, regardless of the lack of full-state measurement,
while learning and implementing an optimal controller. The approach leverages
linear matrix inequality-based observer design method to efficiently search for
observer gains for effective state estimation. Then, approximate dynamic
programming is used to develop an approximate controller that uses simulated
experiences to guarantee the safety and stability of the closed-loop system.
Safety is enforced by adding a recentered robust Lyapunov-like barrier function
to the cost function that effectively enforces safety constraints, even in the
presence of uncertainty in the state. Lyapunov-based stability analysis is used
to guarantee uniform ultimate boundedness of the trajectories of the
closed-loop system and ensure safety. Simulation studies are performed to
demonstrate the effectiveness of the developed method through two real-world
safety-critical scenarios, ensuring that the state trajectories of a given
system remain in a given set and obstacle avoidance.
