Why enroll

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.

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Course content

The course is readily available, allowing learners to start and complete it at their own pace.

Behavioural Theory of Systems with a View Toward Data Driven Control

25 Lectures

784 min

Course Introduction - Behavioural Theory of Systems with a View Toward Data Driven Control
Preview
3 min
Introduction
31 min
Dynamical systems in the behavioural setting
33 min
Ordinary differential and difference equations : Kernel
33 min
Equivalent kernel representations
32 min
Unimodular transformations, equivalent behaviours - sufficient condition
31 min
Polynomial matrices: Aryabhatta-Bezout identity, upper triangular form
34 min
Example- solution of system of differential equations using back substitution
31 min
Solving scalar ordinary differential equations, equivalent behaviours
33 min
Solving multivariable system of differential equations
31 min
Equivalent behaviours: necessary condition for autonomous systems proof
36 min
Equivalent Behaviours: non-autonomous systems proof, input-output partitioning
34 min
Annihilator submodule and associated behaviour
30 min
Elimination Theory introduction, Fundamental principle of algebraic analysis
33 min
Proof of Fundamental principle of algebraic analysis
33 min
Proof revisited: Fundamental principle of Algebraic analysis
30 min
Elimination Theory proof with example
35 min
Elimination examples
31 min
Controllability definition in the behavioural framework
36 min
Equivalent conditions for controllability proof
33 min
More equivalent conditions for controllability
32 min
Moving from controllability to observability
32 min
Observability Continued
33 min
Behavioural Pole Placement
29 min
Identification Basics
35 min

Course details

This course introduces a modern way of designing control systems using data instead of mathematical models. Traditionally, control design requires building an accurate model of the system using equations derived from physics or experiments. In many real-world systems, this is difficult, time-consuming, or even impossible. Data-driven control overcomes this challenge by directly using measured input–output data.The course begins with the behavioural approach to systems theory, where the focus is on how a system behaves rather than on its internal equations. Students will learn how a system can be described through the set of all possible trajectories it can generate, and why this viewpoint is powerful for data-based methods.Next, the course explains how behavioural theory naturally leads to data-driven control techniques. Students will see how controllers can be designed and system properties can be analyzed using only data collected from experiments, without identifying an explicit model.A key concept covered in detail is persistency of excitation, which explains what kind of data is needed to reliably represent system behavior. The course builds intuition on why rich and informative data is essential for successful control design.By the end of the course, students will understand the fundamental ideas, tools, and limitations of data-driven control, and will be able to appreciate how these methods are applied to modern engineering systems where modeling is difficult or uncertain.

Source: NPTEL IIT Bombay [Youtube Channel]

Course suitable for

Automotive
Electrical
Engineering & Design
Project Management
Research & Developmnet

Key topics covered

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

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