This work proposes a robust optimal and control estimation strategy for a broad class of nonlinear processes with uncertain variables and actuator constraints. Using combination of a high-gain observer with a bounded robust optimal state feedback controller synthesized via Lyapunov's direct method and the inverse optimal approach, we construct a bounded robust near-optimal dynamic output feedback controller with well-characterized performance and stability properties. The controller enforces, in the presence of active constraints, exponential stability and robust asymptotic output tracking with arbitrary degree of attenuation of the effect of the uncertainty on the output of the closed-loop system. In addition, the controller design yields an explicit and intuitive characterization of the regions in state space where the aforementioned properties are guaranteed. The developed controller is successfully applied to an exothermic chemical reactor.