In most real life applications Mathematics not only face the challenge of modeling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.

And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.

In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.

The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:
1. Inverse design for sonic boom minimization: the turnpike property,
2. Actuator location for noise reduction: randomization and averaging,
3. Collective behavior: guidance by repulsion.

We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.