# Behavioural Theory of Systems with a View Toward Data Driven Control

- Institution: IIT Bombay
- Department: Electrical Engineering
- Teacher: Prof. Debasattam Pal
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108101587)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108101587)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Week 01: Lecture 01: Introduction](https://invisiblenetwork.ai/learn/nptel/108101587/d7357e22b3fb) (Video)
2. [Week 01: Lecture 02: Dynamical systems in the behavioural setting](https://invisiblenetwork.ai/learn/nptel/108101587/0ac9a1c3615d) (Video)
3. [Week 01: Lecture 03: Ordinary differential and difference equations : Kernel representation](https://invisiblenetwork.ai/learn/nptel/108101587/5428480a0725) (Video)
4. [Week 01: Lecture 04: Equivalent kernel representations](https://invisiblenetwork.ai/learn/nptel/108101587/8278cd59f2ac) (Video)
5. [Week 01: Lecture 05: Unimodular transformations, equivalent behaviours - sufficient condition](https://invisiblenetwork.ai/learn/nptel/108101587/2c6464a49e9f) (Video)
6. [Week 02: Lecture 06: Polynomial matrices: Aryabhatta-Bezout identity, upper triangular form](https://invisiblenetwork.ai/learn/nptel/108101587/3ec45839ce63) (Video)
7. [Week 02: Lecture 07: Example- solution of system of differential equations using back substitution](https://invisiblenetwork.ai/learn/nptel/108101587/e47a1489f4f2) (Video)
8. [Week 02: Lecture 08: Solving scalar ordinary differential equations, equivalent behaviours](https://invisiblenetwork.ai/learn/nptel/108101587/099436ab67af) (Video)
9. [Week 02: Lecture 09: Solving multivariable system of differential equations](https://invisiblenetwork.ai/learn/nptel/108101587/50dca3828472) (Video)
10. [Week 02: Lecture 10: Equivalent behaviours: necessary condition for autonomous systems proof](https://invisiblenetwork.ai/learn/nptel/108101587/c692153a5035) (Video)
11. [Week 03: Lecture 11: Equivalent Behaviours: non-autonomous systems proof, input-output partitioning](https://invisiblenetwork.ai/learn/nptel/108101587/b9308700e946) (Video)
12. [Week 03: Lecture 12: Annihilator submodule and associated behaviour](https://invisiblenetwork.ai/learn/nptel/108101587/8ac6a21055ad) (Video)
13. [Week 03: Lecture 13: Elimination Theory introduction, Fundamental principle of algebraic analysis](https://invisiblenetwork.ai/learn/nptel/108101587/5ad848a57251) (Video)
14. [Week 03: Lecture 14: Proof of Fundamental principle of algebraic analysis](https://invisiblenetwork.ai/learn/nptel/108101587/fa6171c38446) (Video)
15. [Week 03: Lecture 15: Proof revisited: Fundamental principle of Algebraic analysis](https://invisiblenetwork.ai/learn/nptel/108101587/fc7c57f7dd72) (Video)
16. [Week 04: Lecture 16: Elimination Theory proof with example](https://invisiblenetwork.ai/learn/nptel/108101587/400de67985ab) (Video)
17. [Week 04: Lecture 17: Elimination examples](https://invisiblenetwork.ai/learn/nptel/108101587/0691ad8ead1b) (Video)
18. [Week 04: Lecture 18: Controllability definition in the behavioural framework](https://invisiblenetwork.ai/learn/nptel/108101587/02fa227aec34) (Video)
19. [Week 04: Lecture 19: Equivalent conditions for controllability proof](https://invisiblenetwork.ai/learn/nptel/108101587/d1594359388a) (Video)
20. [Week 04: Lecture 20: More equivalent conditions for controllability](https://invisiblenetwork.ai/learn/nptel/108101587/6b02f6815515) (Video)
21. [Week 05: Lecture 21: Moving from controllability to observability](https://invisiblenetwork.ai/learn/nptel/108101587/f48fc6f0176d) (Video)
22. [Week 05: Lecture 22: Observability Continued](https://invisiblenetwork.ai/learn/nptel/108101587/36504c97f06c) (Video)
23. [Week 05: Lecture 23: Behavioural Pole Placement](https://invisiblenetwork.ai/learn/nptel/108101587/99f2bb67453c) (Video)
24. [Week 05: Lecture 24: Identification Basics](https://invisiblenetwork.ai/learn/nptel/108101587/18d61ef9313d) (Video)
25. [Week 05: Lecture 25: The Most Powerful Unfalsified Model (MPUM)](https://invisiblenetwork.ai/learn/nptel/108101587/a7ff9877fb32) (Video)
26. [Week 06: Lecture 26: MPUM for LTI systems: Uniqueness and construction approach](https://invisiblenetwork.ai/learn/nptel/108101587/d3a03cbbd15a) (Video)
27. [Week 06: Lecture 27: Construction approach of MPUM continued](https://invisiblenetwork.ai/learn/nptel/108101587/6ce10de94f1f) (Video)
28. [Week 06: Lecture 28: MPUM construction recalled](https://invisiblenetwork.ai/learn/nptel/108101587/436bca9445c4) (Video)
29. [Week 06: Lecture 29: Some simple numerical examples](https://invisiblenetwork.ai/learn/nptel/108101587/29e55a204517) (Video)
30. [Week 06: Lecture 30: Finding annhilators and hence kernel representation matrix from data](https://invisiblenetwork.ai/learn/nptel/108101587/f88ee194a440) (Video)
31. [Week 07: Lecture 31: Identification of the behaviour using a single trajectory of finite length](https://invisiblenetwork.ai/learn/nptel/108101587/bad088c579f8) (Video)
32. [Week 07: Lecture 32: Single finite length trajectory based identification continued](https://invisiblenetwork.ai/learn/nptel/108101587/a250fe227c4b) (Video)
33. [Week 07: Lecture 33: More discussions on single finite length trajectory based identification](https://invisiblenetwork.ai/learn/nptel/108101587/447f61c67c6f) (Video)
34. [Week 07: Lecture 34: Proof of fundamental lemma of data-driven control](https://invisiblenetwork.ai/learn/nptel/108101587/0ff553c14183) (Video)
35. [Week 07: Lecture 35: Proof of fundamental lemma continued](https://invisiblenetwork.ai/learn/nptel/108101587/bb902d1e42ca) (Video)
36. [Week 08: Lecture 36: Some consequences of fundamental lemma discussed](https://invisiblenetwork.ai/learn/nptel/108101587/17df5aec1386) (Video)
37. [Week 08: Lecture 37: Finding low rank approximations of data Hankel matrices using SVD](https://invisiblenetwork.ai/learn/nptel/108101587/c199e57e21f0) (Video)
38. [Week 08: Lecture 38: Towards data-driven simulation](https://invisiblenetwork.ai/learn/nptel/108101587/43bb281ccae9) (Video)
39. [Week 08: Lecture 39: Data-driven simulation continued & data-driven stability analysis](https://invisiblenetwork.ai/learn/nptel/108101587/bef2a78c7130) (Video)
40. [Week 08: Lecture 40: Data-driven Control: Stabilization by state feedback](https://invisiblenetwork.ai/learn/nptel/108101587/5b8c41cec0d0) (Video)
41. [Live Session 20-03-2025](https://invisiblenetwork.ai/learn/nptel/108101587/d7357e22b3fb-2) (Video)
42. [Live Session 15-04-2025](https://invisiblenetwork.ai/learn/nptel/108101587/0ac9a1c3615d-2) (Video)