Learn · Behavioural Theory of Systems with a View Toward Data Driven Control
Lecture 1 of 42week-01
Week 01: Lecture 01: Introduction
Prof. Debasattam Pal · IIT Bombay
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- Behavioural Theory of Systems with a View Toward Data Driven Control, IIT Bombay (at NPTEL)
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All the lectures
- Week 01: Lecture 01: Introduction
- Week 01: Lecture 02: Dynamical systems in the behavioural setting
- Week 01: Lecture 03: Ordinary differential and difference equations : Kernel representation
- Week 01: Lecture 04: Equivalent kernel representations
- Week 01: Lecture 05: Unimodular transformations, equivalent behaviours - sufficient condition
- Week 02: Lecture 06: Polynomial matrices: Aryabhatta-Bezout identity, upper triangular form
- Week 02: Lecture 07: Example- solution of system of differential equations using back substitution
- Week 02: Lecture 08: Solving scalar ordinary differential equations, equivalent behaviours
- Week 02: Lecture 09: Solving multivariable system of differential equations
- Week 02: Lecture 10: Equivalent behaviours: necessary condition for autonomous systems proof
- Week 03: Lecture 11: Equivalent Behaviours: non-autonomous systems proof, input-output partitioning
- Week 03: Lecture 12: Annihilator submodule and associated behaviour
- Week 03: Lecture 13: Elimination Theory introduction, Fundamental principle of algebraic analysis
- Week 03: Lecture 14: Proof of Fundamental principle of algebraic analysis
- Week 03: Lecture 15: Proof revisited: Fundamental principle of Algebraic analysis
- Week 04: Lecture 16: Elimination Theory proof with example
- Week 04: Lecture 17: Elimination examples
- Week 04: Lecture 18: Controllability definition in the behavioural framework
- Week 04: Lecture 19: Equivalent conditions for controllability proof
- Week 04: Lecture 20: More equivalent conditions for controllability
- Week 05: Lecture 21: Moving from controllability to observability
- Week 05: Lecture 22: Observability Continued
- Week 05: Lecture 23: Behavioural Pole Placement
- Week 05: Lecture 24: Identification Basics
- Week 05: Lecture 25: The Most Powerful Unfalsified Model (MPUM)
- Week 06: Lecture 26: MPUM for LTI systems: Uniqueness and construction approach
- Week 06: Lecture 27: Construction approach of MPUM continued
- Week 06: Lecture 28: MPUM construction recalled
- Week 06: Lecture 29: Some simple numerical examples
- Week 06: Lecture 30: Finding annhilators and hence kernel representation matrix from data
- Week 07: Lecture 31: Identification of the behaviour using a single trajectory of finite length
- Week 07: Lecture 32: Single finite length trajectory based identification continued
- Week 07: Lecture 33: More discussions on single finite length trajectory based identification
- Week 07: Lecture 34: Proof of fundamental lemma of data-driven control
- Week 07: Lecture 35: Proof of fundamental lemma continued
- Week 08: Lecture 36: Some consequences of fundamental lemma discussed
- Week 08: Lecture 37: Finding low rank approximations of data Hankel matrices using SVD
- Week 08: Lecture 38: Towards data-driven simulation
- Week 08: Lecture 39: Data-driven simulation continued & data-driven stability analysis
- Week 08: Lecture 40: Data-driven Control: Stabilization by state feedback
- Live Session 20-03-2025
- Live Session 15-04-2025