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Adaptive Control Systems

Contents of the course

  1. The role of adaptive control in automation engineering. Insufficiency of the basic model-based closed-loop control scheme; the need for robustness, adaptation to uncertain systems or systems that change in time. Classic adaptive schemes, e.g. gain scheduling
  2. Off-line vs. online adaptive control. Direct vs. indirect adaptive control schemes.
  3. Recursive identification schemes: recursive least squares, exponentially weighted LS and their properties.
  4. Classic control schemes. Classic schemes for stabilization, control, and reference following of discrete-time LTI systems.
  5. Indirect online methods: decoupling the problem of robust control as a tool for the design of non-linear controllers.
  6. Modern direct methods: Virtual Reference Feedback Tuning.


The prerequisite of the course is a working knowledge of calculus, linear algebra, and control theory (prior exposition to an introductory course on control theory, typically Fondamenti di Automatica will be sufficient). Prior attendance of the course Data Driven System Modelling is for sure profitable, but is not required. Some results which are not usually taught in basic courses will be reviewed when needed.

Logistics for Spring 2022

The course will be taught in English. The lecture schedule will be reported below as soon as it becomes available:

Day Time Place

Office hours will be scheduled during the first lecture (please send an email before). But if you will attend the course and you wish to discuss the material seen in class or ask questions, I will be happy to arrange other meetings at your convenience.

The examination will be written (no books or notes allowed) and oral, at fixed sessions. The written test will be in English, and the oral examination will be in English or Italian, at your choice.

Learning material

File Comments
linsys_review.pdf 0. A short and fast-paced review of some essential facts in continuous-time system theory. It contains all you need to recall to attend the course.
tank_example.pdf 1. Tank example.
to come 2. Linear algebra review.
to come 3. Discrete time linear systems in state space form.
to come 4. Control with state-space models: design of static feedback and Luenberger observer, separation principle.
ztransform.pdf 5. Review of discrete-time linear systems as maps; unilateral Z transforms.
polynomials.pdf 6. Polynomials, g.c.d., extended Euclid's algorithm, and Diophantine equations.
polycontrol.pdf 7. Control, reference tracking and disturbance rejection with the Diophantine equation.
convergence.pdf 8. Recursive Least Squares and asymptotic analysis of the non-weighted LS estimate.
str_stability.pdf 9. Stability and reference tracking of the self-tuning regulator.
To come Here you will sooner or later find a "compact" and agile set of lecture notes for the course; they will be inserted and grown as the course goes on, week after week.
Official textbook Karl J. Astrom and Bjorn Wittenmark, Adaptive Control, 2nd ed., Dover Publications, 2008.
VRFT website Virtual Reference Feedback Tuning home page: learning material on the VRFT method.