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Course10810158742 lectures

Behavioural Theory of Systems with a View Toward Data Driven Control

Prof. Debasattam Pal · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Week 01: Lecture 01: Introduction Video
  2. Week 01: Lecture 02: Dynamical systems in the behavioural setting Video
  3. Week 01: Lecture 03: Ordinary differential and difference equations : Kernel representation Video
  4. Week 01: Lecture 04: Equivalent kernel representations Video
  5. Week 01: Lecture 05: Unimodular transformations, equivalent behaviours - sufficient condition Video

week-02

  1. Week 02: Lecture 06: Polynomial matrices: Aryabhatta-Bezout identity, upper triangular form Video
  2. Week 02: Lecture 07: Example- solution of system of differential equations using back substitution Video
  3. Week 02: Lecture 08: Solving scalar ordinary differential equations, equivalent behaviours Video
  4. Week 02: Lecture 09: Solving multivariable system of differential equations Video
  5. Week 02: Lecture 10: Equivalent behaviours: necessary condition for autonomous systems proof Video

week-03

  1. Week 03: Lecture 11: Equivalent Behaviours: non-autonomous systems proof, input-output partitioning Video
  2. Week 03: Lecture 12: Annihilator submodule and associated behaviour Video
  3. Week 03: Lecture 13: Elimination Theory introduction, Fundamental principle of algebraic analysis Video
  4. Week 03: Lecture 14: Proof of Fundamental principle of algebraic analysis Video
  5. Week 03: Lecture 15: Proof revisited: Fundamental principle of Algebraic analysis Video

week-04

  1. Week 04: Lecture 16: Elimination Theory proof with example Video
  2. Week 04: Lecture 17: Elimination examples Video
  3. Week 04: Lecture 18: Controllability definition in the behavioural framework Video
  4. Week 04: Lecture 19: Equivalent conditions for controllability proof Video
  5. Week 04: Lecture 20: More equivalent conditions for controllability Video

week-05

  1. Week 05: Lecture 21: Moving from controllability to observability Video
  2. Week 05: Lecture 22: Observability Continued Video
  3. Week 05: Lecture 23: Behavioural Pole Placement Video
  4. Week 05: Lecture 24: Identification Basics Video
  5. Week 05: Lecture 25: The Most Powerful Unfalsified Model (MPUM) Video

week-06

  1. Week 06: Lecture 26: MPUM for LTI systems: Uniqueness and construction approach Video
  2. Week 06: Lecture 27: Construction approach of MPUM continued Video
  3. Week 06: Lecture 28: MPUM construction recalled Video
  4. Week 06: Lecture 29: Some simple numerical examples Video
  5. Week 06: Lecture 30: Finding annhilators and hence kernel representation matrix from data Video

week-07

  1. Week 07: Lecture 31: Identification of the behaviour using a single trajectory of finite length Video
  2. Week 07: Lecture 32: Single finite length trajectory based identification continued Video
  3. Week 07: Lecture 33: More discussions on single finite length trajectory based identification Video
  4. Week 07: Lecture 34: Proof of fundamental lemma of data-driven control Video
  5. Week 07: Lecture 35: Proof of fundamental lemma continued Video

week-08

  1. Week 08: Lecture 36: Some consequences of fundamental lemma discussed Video
  2. Week 08: Lecture 37: Finding low rank approximations of data Hankel matrices using SVD Video
  3. Week 08: Lecture 38: Towards data-driven simulation Video
  4. Week 08: Lecture 39: Data-driven simulation continued & data-driven stability analysis Video
  5. Week 08: Lecture 40: Data-driven Control: Stabilization by state feedback Video

Live Session

  1. Live Session 20-03-2025 Video
  2. Live Session 15-04-2025 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Electrical Engineering
Teacher
Prof. Debasattam Pal
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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