The course aims at providing students of the Management Engineering M.Sc. program with methods and tools for modelling dynamical systems in the different forms useful for control design and dynamic decision making. To do this, students will be shown how these models can be employed as a basis to design predictors of future system states and outputs that may offer forecasting capabilities. Then, the identified models will be used in closed-loop with optimal controllers with the aim of modelling different decision-making and planning processes that may occur in the domains of interest and explore their performance over a finite and infinite time horizon. Many practical examples of interest from different economical/production/management contexts will be employed to prove their impact in the application domains of interest for the students. 

The course includes:

• Lecture sessions: they aim at illustrating, sharing and discussing models, conceptual frameworks, tools and empirical evidence and show, with numerical examples, how to master the presented tools;
• Computer labs: to practice the methods with hands-on experiences using the Matlab/Simulink environment;
• Final project: to be carried out in small teams (3 students at most), and aimed to practically experiment the learnt concept in an application-oriented framework chosen among those of interest for the group.

At the end of the couse, students are expected to:

- be able of building dynamical models from input/output data, both with time and frequency domain representations making use of appropriate model-identification methods;

- be able of design predictors for both input/output models and state-space ones;

- be able of setting up an optimal control problem to model dynamic decision making processes, and apply them to examples taken from real applications.

COURSE DETAILED PROGRAM

1. From data to models: Data-based identification and estimation problems (examples from various application domains). Model representations of dynamical systems in time and frequency domains. Models for classification, prediction, control and simulation. Main issues related to data-processing techniques for dynamical sytems modelling.
2. Model Identification: Input/Output black-box identification: the Prediction Error Minimization (PEM) paradigm. Identification of I/O models via LS (Least Squares) and ML (Maximum likelihood) methods. Spectral estimation and transfer-function parameterization of the frequency response. A simple approach to state-space identification.
3. State/Output prediction Prediction methods from I/O models (Kolmogorov-Wiener theory). State estimation of a dynamical systems: Kalman filtering, prediction and regularization. One-step ahead predictors and multi-step prediction. Convergence and stability properties of the predictor. Comparison with I/O prediction. Use of the Kalman filter for the estimation of uncertain parameters. Overview of the use of prediction methods in control systems.
4. Optimal control of Linear and Time Invariant (LTI) dynamical systems: Optimality criterion. Linear-quadratic control over finite and infinite time horizon. LQ cost function: multi-objective interpretation. Steady-state LQR control. Hints to LQG control. Examples of optimal control problems in the context of economical and production systems.

Basic knowledge of dynamical systems and control (e.g., those presented in the "Fondamenti di Automatica" course of B.Sc. in Management Engineering).

The exam will have a written part, which will cover the theory and require the solution of some numerical exercises and a group project assignment (a group will be made at most of 3 students), at the end of which a public presentation of the results will be given to the class by each group.

The written exam will make 70% of the final grade and the project the remaining 30%. Both written exam and group project work are mandatory for each student.

Students, in the exam, will be asked to demonstrate their understanding of the methods and tools presented in the course, and their ability to apply them consistently to a practical case. In the written exam, students will be asked to apply structured reasoning and to perform the needed steps that allow obtaining the final results, providing adequate motivation for each of them. Clarity and conciseness, together with a competent use of the technical terminology will also be object of evaluation.

In the project, students will be asked to fruifully carry out team work, developing the organization and work-sharing skills needed to perform the different tasks. They will be asked to face a simple yet realistic problem, model it appropriately and apply the concepts and methods learnt in the course autonomously. Further, they will be asked to concisely present the results of their work to both the teacher and their fellow students and be able to answer questions and motivate their design choices.

This book covers all the course program except for the Optimal Control part. It has a lot of additional material that will not be covered in the couse. The book is available among the online resources of the Politecnico di Milano.

This book covers many topics, the one of interest for this course is Optimal Control.