This paper considers robust formulations for the constrained control of systems under uncertainty. The underlying model is nonlinear and stochastic. A mean-variance robustness framework is adopted. We consider formulations to ensure feasibility over the entire domain of the uncertain parameters. However, strict Feasibility may not always be possible, and can also be very expensive. We consider two alternative approaches to address feasibility. Flexibility in the operational conditions is provided via a penalty framework. The robust strategies are rested on a dynamic optimization problem arising from a chemical engineering application.