CP241 - Applied Linear and Nonlinear Control (ALNC) [Mathworks-IISc Collaboration]
This is a postgraduate-level course offered at the Centre for Cyber-Physical Systems (CPS), IISc Bengaluru, in collaboration with MathWorks. The course focuses on bridging advanced control theory with real-world robotic systems. Through MATLAB, Simulink, ROS2, and Motion Capture-based experiments, students develop a deep understanding of linear and nonlinear dynamics, stability theory, optimal control, and safety-critical control for modern autonomous systems.
Course materials from the previous years course is available here.
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