Behavioural Theory of Systems with a View Toward Data Driven Control

This course helps you learn how to design control systems directly from data, without building complex mathematical models. It gives a clear and practical understanding of modern, data-driven control methods used in real-world systems. The concepts are simple, powerful, and highly useful for both industry and research.

• Course Introduction

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

• Introduction

• Dynamical systems in the behavioural setting

• Ordinary differential and difference equations : Kernel

• Equivalent kernel representations

• Unimodular transformations, equivalent behaviours – sufficient condition

• Polynomial matrices: Aryabhatta–Bezout identity, upper triangular form

• Example – solution of system of differential equations using back substitution

• Solving scalar ordinary differential equations, equivalent behaviours

• Solving multivariable system of differential equations

• Equivalent behaviours: necessary condition for autonomous systems proof

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

• Annihilator submodule and associated behaviour

• Elimination Theory introduction, Fundamental principle of algebraic analysis

• Proof of Fundamental principle of algebraic analysis

• Proof revisited: Fundamental principle of Algebraic analysis

• Elimination Theory proof with example

• Elimination examples

• Controllability definition in the behavioural framework

• Equivalent conditions for controllability proof

• More equivalent conditions for controllability

• Moving from controllability to observability

• Observability Continued

• Behavioural Pole Placement

• Identification Basics