Workshop on


March 20th — 23rd

SLTC - Padukka, Sri Lanka


With the increasing complexity of engineering applications and gadgets, more sophisticated mathematical tools are required to analyze dynamical systems and synthesize control algorithms. This has inevitably led to much development in the field of nonlinear control in the past two decades or more. A part of this development has been built on the foundations of differential geometry. The workshop will begin with a refresher on preliminary notions of state-space models and then go onto fundamental notions of stability and nonlinear control synthesis. Mechanical systems - serial link robots, wheeled mobile robots, satellites, spacecraft - form a special class of nonlinear systems and the course will introduce the relevant theory pertaining to these systems. A brief appetizer in differential geometry will be provided to whet the appetite of those who wish to delve further in these topics.


Refresher on Linear State Space Control

Basic notions of state space control such as controllability, observability and feedback control. Observers and observer design using pole placement.

Nonlinear Systems

Vector fields, affine in the control nonlinear systems, the Lie derivative and the Lie bracket. Introduction to mechanical systems and the control of such systems: Nonholonomic and holonomic constraints in mechanical systems. Controllability and observability of nonlinear systems.

Stability and Feedback Control

Lyapunov stability, asymptotic stability, relative degree, feedback linearization, and examples. Introduction to rotation matrices and the rigid body attitude control problem.

Estimation and SLAM

Tracking position and orientation of mobile robots in a local coordinate system and the construction of a globally consistent map during navigation and/or task execution by analyzing the sequence of camera images.

Tutorials / Demonstrations

Facilitated by

Workshop Schedule

  • 20/03/2019

  • A refresher on state-space modelling and control

    9:00AM — 10:30AM

    Comparison of frequency-domain and state-space approaches for system modelling; conversion from transfer function to state-space models and vice versa; examples of state-space modelling of practical systems.

    Manukid Parnichkun / AIT

  • Controllability and Observability

    11:00AM — 12:30PM

    Definitions and motivation; deriving the controllability and observability rank tests; the Cayley-Hamilton theorem; the controllable and observable subspaces; the controllable canonical form and the observable canonical form.

    Ravi Banavar / IITB

  • Observers and observer design

    1:30PM — 3:00PM

    Observers and their applications; linear observer design by pole placement method; full order and reduced order observers; observers with exogeneous input; example of observer design.

    Manukid Parnichkun / AIT

  • Balancing control - QUBE – Servo 2

    4:00PM — 5:30PM

    T. Weerakoon / S. Gunawardena

  • 21/03/2019

  • Affine in the control nonlinear systems

    8:30AM — 10:00AM

    Vector fields and relation to differential equations, flow of a vector field as solutions of ODE's - group property of flows, complete flow, the Lie Bracket and its properties, Lie Brackets and coordinate changes, Commutators, Jacobii Identity, and Lie Algebra.

    Srikant Sukumar / IITB

  • Constrained mechanical systems

    10:30AM — 12:00PM

    Examples - the rolling coin, the spherical robot; the notion of integrable and non-integrable distributions; driftless nonholonomic systems and controllability notions; Chow's theorem.

    Ravi Banavar / IITB

  • Nonlinear controllability and observability:

    1:00PM — 2:30PM

    Extending controllability and observability notions to nonlinear systems using Lie brackets and distributions; Application to rigid body motion and motion planning of nonholonomic systems.

    D. H. S. Maithripala / UoP

  • Swing up control - QUBE – Servo 2

    3:00PM — 5:00PM

    T. Weerakoon / S. Gunawardena

  • 22/03/2019

  • Stability

    8:30AM — 10:00AM

    Fundamental definitions of Lyapunov stability, uniform stability, asymptotic stability, global stability; comparison functions - introduce class K, KL, and K_\infty functions and define definiteness, decrescence and radial unboundedness using these; introduce Lyapunov's stability theorems with examples; La Salle invariance principle and specializations with examples.

    Srikant Sukumar / IITB

  • Feedback linearization

    10:30AM — 12:00PM

    Affine in the control (input/output) nonlinear system; relative degree of an output; relationship to linear systems; the Ad operator; transformation of coordinates; the zero dynamics; examples.

    Ravi Banavar / IITB

  • Rigid Body Control

    1:00PM — 2:30PM

    Global representation of rigid body motion; coordinate independent globally defined rigidbody tracking error dynamics; intrinsic PD control; Application to multi rotor UAV attitude stabilization.

    D. H. S. Maithripala / UoP

  • Balancing control - QUANSER Aero

    4:00PM — 5:30PM

    T. Weerakoon / S. Gunawardena

  • 23/03/2019

  • Estimation and The Kalman filter

    8:30AM — 10:00AM

    White noise random process in disturbance and measurement noise; objective function of Kalman filter; Kalman filter gain determination and steady-state solution; example of Kalman filter design of practical systems.

    Manukid Parnichkun / AIT

  • Disturbance Observers

    10:30AM — 12:00PM

    Introduction to Disturbance Observer( DOB) taking a DC motor as an example; extension of the DoB to attain robustness in motion control and its use as a force sensor; Examples of force sensing, bilateral tele-operation, and friction compensation.

    Harsha Abeykoon / AIT


    1:00PM — 2:30PM

    Tracking position and orientation in a local coordinate system by analyzing a sequence of camera images. Construction of a globally consistent map during navigation and/or task execution using vision based techniques.

    Matthew Dailey / AIT

  • SLAM - QUANSER Qbot 2

    4:00PM — 5:30PM

    T. Weerakoon / S. Gunawardena

Resource Persons

Ravi N. Banavar

Srikant Sukumar

Manukid Parnichkun

Matthew N. Dailey

A. M. Harsha S. Abeykoon

D.H.S. Maithripala


Priority will be given to students from IIT-Bombay, AIT Bangkok and students from Sri Lanka in availing of the complete subsidy (local travel, accommodation, and meals). The final list of eligible students would be announced on the website by February 15th, 2019. Those who do not make it to this list would have to pay for all expenses.

Those participants interested in the workshop please contact and register with:

India - Prof. Ravi Banavar (

Thailand - Prof. Manukid Parnichkun (

Sri Lanka - Dr. Tharindu Weerakoon (

For other further information and clarifications please contact:

Sri Lanka - Dr. D.H.S. Maithripala(