Funded as part of the “Strategic Plan 2014-2016” of the University of Trento, this 18-months interdepartmental project aims to enable the scientific interchange among three important expertise available within the University: the mathematical core residing in the Department of Mathematics (MAT), the control engineering core residing in the Industrial Engineering Department (DII), and the engineering applications core residing in the Department of Information Engineering and Computer Science (DISI).

The proposed research starts from the study of the mathematical challenges behind a motivating experiment provided by DISI: the optimal control of a robotic application consisting of an autonomous car. The arising model comprises a complicated mixing of continuous evolution and instantaneous jumps: a so-called **hybrid dynamical evolution.**

The goal of the project is to develop optimal hybrid control results using *Calculus of variations* *and optimal control *techniques where MAT contains the theoretical expertise and DII contains the numerical expertise (a fundamental link between theory and experiments). A new powerful framework for hybrid dynamical system (where DII has expertise) will also be used in combination with MAT to develop new optimal hybrid control solutions using *nonlinear partial differential equations *(such as Hamilton-Jacobi equations) and stochastic hybrid systems at the frontier between *mathematical physics and probability*.