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

Engineering Academy

Engineering Academy

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Course typeWatch to learn anytime
Duration 784 Min
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Language English
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Behavioural Theory of Systems with a View Toward Data Driven Control banner
Preview this course

Behavioural Theory of Systems with a View Toward Data Driven Control

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.

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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 icon

    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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