The mathematical modelling and numerical simulation of complex systems plays a crucial role in real life applications. Very often, the modelling procedure results in solving a set of partial differential equations (PDEs). However, in many realistic applications, the final goal is not only the mathematical modelling and numerical simulation of the complex system (**direct problem**), but rather the optimization or optimal control of the considered process (**inverse problem**).

For instance, in swimming races, the swimmer should optimize his/her stroke while undertaking the least physic al effort; in microelectronics, a given semiconductor device must be designed (for example, by acting on its doping profile) so as to limit power consumption while maximizing some performance index (e.g., the switching speed); in medical surgery, the shape of a by-pass has to be optimized to reduce the vorticity downstream the graft, responsible of a possible new stenosys; in environmental issues, the concentration of toxic substances and pollutants emitted by industrial plants near a town (rather than of contaminants dumped in a river) should be kept below some attention level, without compromising the production rate of the factories involved.

In all these applications, we deal with the

**optimal control of systems governed by PDEs**. The specific objective can actually be formalized in terms of the minimization of a suitable cost functional under the fulfillment of a set of constraints represented by the system of PDEs describing the physical phenomena under investigation.View a list of journal publications and MOX Reports related to optimal control problems.

View a list of theses related to optimal control problems.