Computational methods for data-driven optimal control (1 ECTS, SSD: MAT08)

This course introduces the fundamental ideas and computational methods behind optimal control and data-driven modelling. In this short course, we will study how to incorporate elements of machine learning into optimal control design. The course will focus on fundamentals on optimal control: dynamic optimization, linear-quadratic control, dynamic programming and Pontryagin's maximum principle. Nonlinear optimal control. Approximation methods in high dimensions are also discussed such as polynomial approximation, deep neural networks. Optimization techniques: LASSO regression, stochastic gradient descent, training neural networks. Finally, combining the first two parts, we will study the construction of data-driven schemes for the approximation of high-dimensional nonlinear control laws.