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<!DOCTYPE html>
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<div class="hero-image">
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    <h1 style="font-size:30px"><I><a href ="https://github.com/Abishek92/Lorenz_Attractor">Lorenz Attractor</a></I></h1>
    <p></p>
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        <h3><b>Dynamical Systems:</b></h3>
        Source codes for simulating dynamical systems can be found below.

        <h4><b><i>Lorenz Attractor</b></i></h4>
        <p align = "justify">
        The Lorenz attractor (which is show on the top of this webpage) is a class of dynamical systems that exhibits <a href = "https://en.wikipedia.org/wiki/Chaos_theory">chaotic behaviour</a>.
        A small change in initial conditions can lead to large changes in the solutions. This is popularly known as
        <a href = "https://en.wikipedia.org/wiki/Butterfly_effect">"the butterfly effect</a>".
      </p>

      <p align = "justify">
        The code given <a href = "https://github.com/Abishek92/Lorenz_Attractor"><b>here</b></a> can be run on Matlab/Octave.<br>

        A 3-D plot of the simulation is shown below. <br>
        <img src = "Lorenz_attractor.jpg"><br>
        </p>


      <hr class = "new4">
      <h3><b>Control:</b></h3>
      Source codes for simulating Control techniques in dynamical systems can be found below.
      <h4><b><i>Two Car Vehicle Platoon using Adaptive Control</b></i></h4>
      <p align = "justify">
      Vehicle Platoons are used in transportation for optimizing flow of traffic.
      Current research in autonomous driving also employ the use of vehicle platoons. There are several advanatages such as
      increased fuel economy, reduced traffic congestion.
    </p>
    <p align = "justify">
    The Python code given <a href = "https://github.com/Abishek92/Vehicle_Platoon_Simulation"> <b>here</b></a> simulates a two car platoon. The nominal distance between the platoon is maintained through an
    adaptive control strategy. In addition to this, a Kalman filter is also implemented in order to reduce sensor noise.
    </p>
    <p align = "justify">
    The simulation was written for a couple of RC cars, where the velocity of the cars are given in mm/sec
    and the distance between them which is measured through a noisy ultrasonic sensor is given in mm.
    The Kalman filter simulation is shown below. <br>
    <img src="Platoon_kalman.jpeg"><br>

    </p>
    <p align = "justify">
    The simulation showcasing the convergence of the velocity estimate (which is the adaptive part) and the actual input
    to the second car is given below. <br>
    As the estimate of the velocity converges to the actual value of the velocity of the previous car, the estimate achieves a steady state<br>
    <img src="platoon_adaptive_estimate.jpeg"><br>
    </p>
    <p align = "justify">
      Finally, the plots showing the convergence of the distance between two cars to a constant reference of 200 mm is shown.<br>
      <img src = "platoon_distance_error.jpeg"><br>
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        <h2 class="w3-text-black w3-padding-16"><i class="fa fa-fw w3-margin-right w3-xxlarge w3-text-blue"></i><b>Abishek Chandrasekhar</b></h2>
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          <p><i class="fa fa-graduation-cap w3-margin-right w3-large w3-text-blue"></i><b>Ph.D. candidate</b></p>
          <p><i class="fa fa-book w3-margin-right w3-large w3-text-blue"></i><b>Research: Dynamical Systems and Control Theory</b></p>
          <p><i class="fa fa-institution w3-margin-right w3-large w3-text-blue"></i><a href="https://cps.iisc.ac.in/"><b>Robert Bosch Centre for Cyber-Physical Systems @ IISC</a></b></p>
          <p><i class="fa fa-envelope fa-fw w3-margin-right w3-large w3-text-blue"></i> <a href="mailto:abishek.c@iisc.ac.in"><b>abishek.c@iisc.ac.in</a></b></p>
          <p><i class="fa fa-phone fa-fw w3-margin-right w3-large w3-text-blue"></i><b>+91-8197505290</b></p>
          <p><i class="fa fa-home fa-fw w3-margin-right w3-large w3-text-blue"></i><b>Bangalore, India</b></p>
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