NOC:Behavioural Theory of Systems with a View Toward Data Driven Control

Lecture 1 - Introduction

Lecture 2 - Dynamical systems in the behavioural setting

Lecture 3 - Ordinary differential and difference equations : Kernel representation

Lecture 4 - Equivalent kernel representations

Lecture 5 - Unimodular transformations, equivalent behaviours - sufficient condition

Lecture 6 - Polynomial matrices: Aryabhatta-Bezout identity, upper triangular form

Lecture 7 - Example - Solution of system of differential equations using back substitution

Lecture 8 - Solving scalar ordinary differential equations, equivalent behaviours

Lecture 9 - Solving multivariable system of differential equations

Lecture 10 - Equivalent behaviours: necessary condition for autonomous systems proof

Lecture 11 - Equivalent Behaviours: non-autonomous systems proof, input-output partitioning

Lecture 12 - Annihilator submodule and associated behaviour

Lecture 13 - Elimination Theory introduction, Fundamental principle of algebraic analysis

Lecture 14 - Proof of Fundamental principle of algebraic analysis

Lecture 15 - Proof revisited: Fundamental principle of Algebraic analysis

Lecture 16 - Elimination Theory proof with example

Lecture 17 - Elimination examples

Lecture 18 - Controllability definition in the behavioural framework

Lecture 19 - Equivalent conditions for controllability proof

Lecture 20 - More equivalent conditions for controllability

Lecture 21 - Moving from controllability to observability

Lecture 22 - Observability (Continued...)

Lecture 23 - Behavioural Pole Placement

Lecture 24 - Identification Basics

Lecture 25 - The Most Powerful Unfalsified Model (MPUM)

Lecture 26 - MPUM for LTI systems: Uniqueness and construction approach

Lecture 27 - Construction approach of MPUM (Continued...)

Lecture 28 - MPUM construction recalled

Lecture 29 - Some simple numerical examples

Lecture 30 - Finding annhilators and hence kernel representation matrix from data

Lecture 31 - Identification of the behaviour using a single trajectory of finite length

Lecture 32 - Single finite length trajectory based identification (Continued...)

Lecture 33 - More discussions on single finite length trajectory based identification

Lecture 34 - Proof of fundamental lemma of data-driven control

Lecture 35 - Proof of fundamental lemma (Continued...)

Lecture 36 - Some consequences of fundamental lemma discussed

Lecture 37 - Finding low rank approximations of data Hankel matrices using SVD

Lecture 38 - Towards data-driven simulation

Lecture 39 - Data-driven simulation continued and data-driven stability analysis

Lecture 40 - Data-driven Control: Stabilization by state feedback