Hours:
16 hours (4 credits)

Room:

Aula Riunioni del Dipartimento di Ingegneria dell’Informazione, Via G. Caruso 16, Pisa - Ground Floor

To register to the course, click here

Short Abstract:

The objective of the course is to provide the students with a comprehensive background on the analysis and control of continuous dynamical systems, using a state variable approach in the time domain. The analysis will overview nonlinear dynamics from a qualitative geometric point of view, and advantages/disadvantages of linearization. The full systemic solution of linear systems is addressed, using linear algebra background. Control approaches are based on full state as well as output (static and dynamic) feedback in the deterministic domain. A brief introduction of optimal control is included. Numerical worked examples will accompany the mathematical material.

Course Contents in brief:

1. Part 1: Motivation, main definitions, examples of nonlinear systems (fixed point computation, vector fields), linearization (review of Taylor series and power series).
2. Part 2: Linear systems solution, state transition matrix, Cayley-Hamilton theorem, role of eigenvalues and eigenvectors. Structural properties. Numerical examples
3. Part 3: Full state feedback (regulation, servomechanism), eigensystem assignment, static and dynamic output feedback state reconstruction.
4. Part 4: Optimal control generalities, linear quadratic regulator, Riccati equation and its relationship with Lyapunov stability, robustness of the closed loop system.

Schedule:

1. Day1 – June 10, 2025, 14:00 -18:00
2. Day2 – June 11, 2025, 14:00 -18:00
3. Day3 – June 12, 2025, 14:00 -18:00
4. Day4 – June 13, 2025, 14:00 -18:00