In this thesis, we study two topics related to large-scale sparse estimation and control. In the first topic, we describe a method to eliminate features (variables) in $\ell_{1}$-regularized convex optimization problems. The elimination of features leads to a potentially substantial reduction in computational effort needed to solve such problems, especially for large values of the penalty parameter. Our method is not heuristic: it only eliminates features that are guaranteed to be absent after solving the optimization problem. The feature elimination step is easy to parallelize and can test each feature for elimination independently. Moreover, the computational effort of our method is negligible compared to that of solving the convex problem. We study the case of $\ell_{1}$-regularized least-squares problem (a.k.a. LASSO) extensively and derive a closed-form sufficient condition for eliminating features. The sufficient condition can be evaluated by few vector-matrix multiplications. For comparison purposes, we present a LASSO solver that integrates SAFE with the Coordinate Descent method. We call our method CD-SAFE, and we report the number of computations needed for solving a LASSO problem using CD-SAFE and using the plain Coordinate Descent method. We observe at least a $100$ fold reduction in computational complexity for dense and sparse data-sets consisting of millions of variables and millions of observations. Some of these data-sets can cause memory problems when loaded, or need specialized solvers. However, with SAFE, we can extend LASSO solvers capabilities to treat large-scale problems, previously out of their reach. This is possible, because SAFE eliminates variables and thus portions of our data at the outset, before loading it into our memory. We also show how our method can be extended to general $\ell_{1}$-regularized convex problems. We present preliminary results for the Sparse Support Vector Machine and Logistic Regression problems. In the second topic of the thesis, we derive a method for open-loop control of open channel flow, based on the Hayami model, a parabolic partial differential equation resulting from a simplification of the Saint-Venant equations. The open-loop control is represented as infinite series using differential flatness, for which convergence is assessed. Numerical simulations show the effectiveness of the approach by applying the open-loop controller to irrigation canals modeled by the full Saint-Venant equations. We experiment with our controller on the Gignac Canal, located northwest of Montpellier, in southern France. The experiments show that it is possible to achieve a desired water flow at the downstream of a canal using the Hayami model as an approximation of the real-system. However, our observations of the measured water flow at the upstream controlled gate made us realize some actuator limitations. For example, deadband in the gate opening and unmodeled disturbances such as friction in the gate-opening mechanism, only allow us to deliver piece-wise constant control inputs. This fact made us investigate a way to compute a controller that respects the actuator limitations. We use the CD-SAFE algorithm, to compute such open-loop control for the upstream water flow. We compare the computational effort needed to obtain an open-loop control with certain dynamics using the CD-SAFE algorithm and the plain Coordinate Descent algoirthm. We show that with CD-SAFE we are able to obain an open-loop control signal with cheaper computations.