Course code UPM124
Course title Geometric and numerical methods in control theory
Institution Universidad Politecnica de Madrid
Course address ETS Arquitectura, Avenida Juan de Herrera 4
City Madrid
Minimum year of study 3rd year
Minimum level of English Good
Minimum level of French None
Key words


Euler-Lagrange equations, control systems, robotics, numerical integrators.

Language ENGLISH
Professor responsible MARÍA BARBERO LIÑÁN
Telephone 913366562
Participating professors


Leonardo Colombo (ICMAT-CSIC), David Martín de Diego (ICMAT-CSIC).

Number of places Minimum: 10, Maximum: 30, Reserved for local students: 10



To understand the notion of control systems and the main properties (accessibility, controllability,…)

- To study examples from robotics (rigid bodies, sankeboards, manipulators, satellites, etc).

- To implement/use numerical integrators using MatLab or Python.

- To understand the positive contribution of the geometric approach in control theory.

Programme to be followed


Part 1: Introduction to control systems.

1.1. Control-linear systems.

1.2. Control-affine systems.

1.3. Accessibility, controllability.

1.4. Other interesting problems: trackability, optimality.

Part 2: Introduction to robotics via examples.

2.1. Sankeboard.

2.2. Satellites.

2.3. Multi-link manipulators.

Part 3: Implementation.

3.1. Numerical integrators.

3.2. Programming using Matlab/Python.


Bullo, Lewis. Geometric Control of Mechanical Systems. Modeling, Analysis, and Design for Simple Mechanical Control Systems.


Linear algebra, calculus, differential equations.

Course exam

Project. Study of some practical cases.