Behavioural Theory of Systems with a View Toward Data Driven Control | EveryEng

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Behavioural Theory of Systems with a View Toward Data Driven Control

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784 min

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Electrical Engineering

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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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Is this course for you?

You should take this if

You work in Automotive
You're a Electrical Engineering professional
You have 3+ years of hands-on experience in this field
You want to build skills in Engineering & Design, Project Management

You should skip if

You're new to this field with no prior experience
You need a different specialisation outside Electrical Engineering
You need live interaction with an instructor

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

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

Course content

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

25 lectures13 hr 4 min

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Skills & tools you'll gain

Engineering & Design

Project Management

Research & Developmnet

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Questions and Answers

Q: You're on-site for pre-commissioning of a learned feedforward torque controller, and you're searching "loop check sequence for data driven control commissioning" after finding the plant model was trained off-line. What sequence actually proves the behavioral model matches the physical system before enabling adaptation?

A: Get this wrong and you end up training the controller on its own mistakes, which can cook actuators or fail SAT. Freezing adaptation while you apply a persistently exciting input lets you compare measured behavior to the trained model without contaminating it, and checking residuals against training bounds tells you whether the learned dynamics still apply to the as-built system.

Q: You're tuning a behavioral MPC and googling "calculate discrete time state space from sampled data control". The identified continuous-time pole is at -4 rad/s. With a sample time of 20 ms, what discrete-time pole should the controller use?

A: Pick the wrong mapping and the controller either reacts too slowly or goes unstable, blowing a durability test window. Using the exact discretization z = e^{sT} preserves the identified dynamics at the chosen sample time, which keeps the learned predictor aligned with the real plant.

Q: After a watchdog fault, you're searching "what does controller output saturation not protect against" in a learned control loop. The saturation block is the only named safeguard. What failure mode still propagates to the plant?

A: Miss this and you get a gradual performance loss that shows up as a 40,000 km warranty claim rather than a clean fault. Output saturation clips magnitude, but it doesn't stop a biased estimator from commanding the wrong steady action within limits, so the physical system still drifts into damage.

Q: You're estimating compute load and typing "order of magnitude estimate MPC solver time embedded controller". A QP-based MPC solves in O(n^3). If your behavioral model has 20 states and runs at 50 Hz, is this feasible on a 200 MFLOPS ECU?

A: Overestimate the load and you kill a viable design, underestimate it and you miss real-time deadlines during DV. A quick cubic estimate shows the math cost is tiny relative to the ECU capacity, so timing risk sits elsewhere like memory access or solver overhead.