Courses offered in 2026

CP241 - Applied Linear and Nonlinear Control (ALNC) [Mathworks-IISc Collaboration]

Course Objective

To provide a structured transition from the mathematical modeling of dynamical systems to the implementation of safety-critical, optimal controllers on mobile robots and manipulators.

Module 0: Mathematical Preliminaries

THEORY:

Normed Vector spaces, Continous Functions, Differentiability Class, Lipschitz continuity, Cauchy–Schwarz Inequality, Class-K, Class-KL functions

Module 1: Foundations of Dynamical Systems

THEORY:

Introduction to Dynamical Systems. Linear system modelling. Nonlinear system modelling. Approximation and linearization of nonlinear systems. Brief introduction to other classes of systems.

PRACTICAL LAB:

Experiment Setup: MATLAB and Simulink environment for modelling and simulation of representative linear and nonlinear dynamical systems.

Goals:

• Develop mathematical models of first and second-order linear systems and selected nonlinear systems.

• Simulate system responses for different initial conditions and external inputs.

• Compare the behaviour of linear and nonlinear systems.

• Visualize state trajectories and time responses using MATLAB Live Scripts.

Toolboxes: MATLAB ODE Suite, Simulink

Hardware: N/A (Simulation)

Module 2: System Analysis & Behaviour

THEORY:

Linear Time Invariant (LTI) systems. Solution of linear and nonlinear systems. Numerical solution techniques. Phase space analysis.

PRACTICAL LAB:

Experiment Setup: MATLAB environment utilizing ODE solvers and symbolic tools for numerical analysis and phase-space visualization.

Goals:

• Numerically solve ordinary differential equations using MATLAB ODE solvers.

• Generate and interpret phase portraits for representative dynamical systems.

• Identify equilibrium points and analyze transient behaviour.

• Study the evolution of system trajectories under different initial conditions.

Toolboxes: MATLAB ODE Suite, Symbolic Math Toolbox

Hardware: N/A (Simulation)

Module 3: Stability Analysis of Dynamical and Control Systems

THEORY:

Stability analysis of linear systems using eigenvalues and eigenvectors. Stability analysis of nonlinear systems using 𝜖 − 𝛿 definitions. Direct and Indirect Lyapunov methods. Input-to-State Stability (ISS). ISS-Lyapunov functions. Illustrative examples

PRACTICAL LAB:

Experiment Setup: MATLAB-based simulations with optional deployment on a Reaction Wheel Pendulum platform for experimental validation.

Goals:

• Construct Lyapunov functions for representative dynamical systems.

• Verify stability properties through simulation.

• Visualize regions of attraction and compare stable and unstable behaviours.

• Implement and evaluate stabilization strategies on a Reaction Wheel Pendulum.

Toolboxes: Control System Toolbox, Symbolic Math Toolbox

Hardware: Reaction Wheel Pendulum (optional)

Module 4: Classical & Linear Control Design

THEORY:

Bang-Bang control. PID control. Pole placement. Controllability, reachability and observability.

PRACTICAL LAB:

Experiment Setup: TurtleBot3 and Reactor X200 robotic platforms integrated with MATLAB and Simulink environments.

Goals:

• Design and implement PID and state-feedback controllers.

• Perform trajectory tracking experiments on robotic systems.

• Analyze controllability and observability properties.

• Evaluate controller performance under varying operating conditions.

Toolboxes: Control System Toolbox,Simulink Control Design

Hardware: TurtleBot3, Reactor X200

Module 5: Advance Control Design

THEORY:

Control Lyapunov Functions (CLF), Feedback linearization, Backstepping, Linear Quadratic Regulator (LQR), Model Predictive Control (MPC), Sliding Mode Control (SMC) , Model Reference Adaptive Control (MRAC).

PRACTICAL LAB:

Experiment Setup: TurtleBot3 and Reactor X200 robotic platforms integrated with MATLAB toolboxes for implementing advanced control algorithms.

Goals:

• Implement advanced control strategies such as feedback linearization, backstepping, LQR, MPC, and MRAC.

• Perform trajectory tracking and disturbance rejection experiments.

• Compare controller performance based on tracking accuracy and control effort.

• Evaluate the strengths and limitations of different advanced control techniques.

Toolboxes: Control System Toolbox, MPC Toolbox, Symbolic Math Toolbox

Hardware: TurtleBot3, Reactor X200

Module 6: Constraint-Based Control

THEORY:

Funnel control, Control Barrier Functions (CBF), Safety Filters.

PRACTICAL LAB:

Experiment Setup: TurtleBot3 operating within a Motion Capture (MoCap) arena. Algorithms will be deployed using the Optimization Toolbox for real-time Quadratic Programming and the ROS Toolbox for hardware communication.

Goals:

• Define safe operational sets and formulate Control Barrier Functions (CBFs) for mobile robot navigation.

• Implement optimization-based safety filters for obstacle avoidance.

• Validate safe navigation in environments containing static and dynamic obstacles.

• Analyze the trade-off between task performance and safety constraints.

Toolboxes: Optimization Toolbox, Symbolic Math Toolbox, ROS Toolbox

Hardware: TurtleBot3, MoCap