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| Academic Year |
2024/2025 |
| Name |
Dott. - MI (1380) Ingegneria dell'Informazione / Information Technology |
| Programme Year |
1 |
| ID Code |
062776 |
| Course Title |
DEALING WITH UNCERTAINTY IN DATA-BASED LEARNING |
| Course Type |
MONO-DISCIPLINARY COURSE |
| Credits (CFU / ECTS) |
5.0 |
| Course Description |
The course covers the problem of making inferences from data when the system or phenomenon generating the data is (totally or partially) unknown, but it is possible to obtain noise-corrupted measurements of the inputs and outputs. The Set Membership (SM) framework described in the course aims to learn models from such data while dealing with limited information and/or computation, such as in presence of samples affected by bounded noise, finite datasets, and/or unmodelled dynamics. SM approaches allow one to derive uncertainty bounds and model optimality metrics in such problems. The content is divided in five chapters:
1. General formulation of the inference problem in the Set Membership framework: bounded noise models, fundamental results in SM parametric estimation, validation of a-priori assumptions, feasible sets and intervals.
2. The second part pertains to SM techniques in system identification: model structures for linear and non-linear systems, linear-in-parameters models, handling unmodeled dynamics, feasible systems sets and uncertainty bounds, non-parametric models of non-linear functions and systems, guaranteed prediction and simulation errors, stability results.
3. The third part covers the problem of filter/observer design from data, i.e., given an unknown dynamic system, algorithms to estimate state variables of interest given a finite set of input/output measurements. The concept of direct virtual sensor (DVS) is introduced, and techniques for the derivation of optimal DVS for linear, LPV and Nonlinear systems are presented. Guaranteed bounds on the estimation error and the accuracy dependance on the size of the data sets are provided.
4. The fourth part presents frameworks for the design of decision and control strategies from data (learning-based control laws design), including formulations for linear systems considering reference models, inverse-based controllers for non-linear systems, and learning-based predictive controllers.
5. The final part introduces the use of SM techniques to tackle black-box optimization problems, where the cost and/or constraint functions are not available analytically. It is shown how the SM framework is applied to iteratively learn and optimize the cost function, while also learning the constraints and trading off exploitation, exploration, and safety during the optimization task.
Case studies and real-world applications will be presented for each part. In particular, the following hands-on exercise sessions will be held:
- Derivation of feasible parameter sets for linear-in-parameters models.
- Derivation of optimal feasible intervals for nonlinear functions and systems.
- Solution of black-box, constrained optimization problem using SM surrogate modes. |
| Scientific-Disciplinary Sector (SSD)
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SSD Code
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SSD Description
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CFU
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ING-INF/04
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SYSTEMS AND CONTROL ENGINEERING
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5.0
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Alphabetical group
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Name
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Teaching Assignment Details
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From (included)
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To (excluded)
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A
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ZZZZ
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Ruiz Palacios Fredy Orlando, Fagiano Lorenzo Mario, Novara Carlo
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