Learning for Dynamics and Control (6 credits): This course is offered at the 1st year of master degree in Automation Engineering and Robotics. The course aims at providing students with advanced knowledge in the field of automatic control with special emphasis to the application of optimization methods. Actually many problems in identification and control can be interpreted as optimization problems and advanced computational tools can be employed for their solution, also in real time. Space is dedicated to "Markov Decision Processes" which are a basis for the understanding of modern Reinforcement Learning methods.
The course, and the exam, make a strong case for the use of computing platform so that the student can test on "practical" problems, though in simulations, the power of the various methods taught, and the difficulties (and satisfaction) of moving from theory to application.
Model Identification and Estimation (6 credits): The course "Model Identification and Estimation" provides students in Management Engineering with a comprehensive foundation in system theory, optimization techniques, and statistical modeling. The course begins with an introduction to system observability and controllability, transitioning to eigenvalue assignment and observer design.
Optimization methods are a core focus, including unconstrained and constrained problems, quadratic forms, Lagrange multipliers, and numerical optimization techniques such as the Karush-Kuhn-Tucker (KKT) conditions. Practical applications, such as the Markowitz portfolio problem, shadow prices, and the use of MATLAB's commands for optimization, are explored in detail.
The course delves into estimation techniques, emphasizing Bayesian estimation, the Bayesian linear estimator, and the Kalman filter, which are revisited in multiple sessions for thorough understanding. Parametric estimation is presented alongside elements of machine learning, providing a modern perspective on model identification. A significant portion of the course addresses stochastic processes and time series analysis, Wold's representation theorem, and ARMA models, with practical MATLAB-based exercises.
System Identification (6 credits): The "System Identification" course introduces students of Mathematical Engineering to advanced methods for modeling and analyzing dynamic systems. The curriculum covers optimal control formulation, variational optimization, and iterative methods such as gradient and Newton approaches. Bayesian estimation, Kalman filtering, and their extensions are thoroughly examined, with an emphasis on theoretical properties and practical applications.
Parametric estimation is explored through concepts like minimum variance estimators, BLUE, and maximum likelihood estimation. Students also learn stochastic process modeling, including stationarity, ergodicity, Wold decomposition, and time series representation. Practical challenges, such as noise-robust identification and Wiener-Hopf applications, are addressed.
The course integrates concepts from Markov chains, Monte Carlo simulation, and stochastic dynamic programming, bridging the gap between classical control, reinforcement learning, and model predictive control (MPC). Hands-on MATLAB sessions using the System Identification and MPC toolboxes solidify theoretical insights, preparing students to tackle real-world identification and control challenges.