# **Post Graduate Courses**

**Program Core Courses :**

**ELL700 Linear Systems Theory (3-0-0)**

Review of matrix algebra, state variable modelling of continuous
and discrete time systems, linearization of state equations, solution
of state equations of linear time-invariant and timevarying systems,
Controllability and observability of dynamical systems, Minimal
realization of linear systems and canonical forms, Lyapunov's stability
theory for linear dynamical systems, State Feedback controllers,
Observer and Controller design.

**ELL701 Mathematical Methods in Control (3-0-0)**

Linear Spaces - Vectors and Matrices, Transformations, Norms - Vector
and Matrix norms, Matrix factorization, Eigenvalues and Eigenvectors
and Applications, Singular Value Decomposition and its Applications,
Projections, Least Square Solutions. Probability, Random Variables,
Probability distribution and density functions, Joint density and
Conditional distribution, Functions of random variables, Moments,
characteristic functions, sequence of random variables, Correlation
matrices and their properties, Random processes and their properties,
Response of Linear systems to stochastic inputs, PSD theorem.

**ELL702 Nonlinear Systems (3-0-0)**

Introduction to nonlinear systems: Examples of phenomena, models
& derivation of system equations. Fundamental properties: Existence
& uniqueness, Dependence on initial conditions & parameters.
Phase plane analysis. Limit cycles & oscillations. Describing function
method and applications. Circle criterion. Lyapunov stability of
autonomous systems. Perturbation theory & Averaging. Singular
perturbation model and stability analysis. Basic results on Lie algebra.
Controllability and Observability of nonlinear systems. Bifurcations.
Chaos. Synchronization.

**ELL703 Optimal Control Theory (3-0-0)**

Maximization of functionals of a single and several functions using
calculus of variations, Constrained extremals, Euler-Lagrange Equation,
Necessary conditions for optimal control, Pontryagin's minimum
principle and state inequality constraints, Minimum time problems,
Minimum control effort problems, Linear quadratic regulator problems,
Riccati Equation, Singular intervals in optimal control problems, The
principle of optimality, Application of the principle of optimality to
decision making, Dynamic programming applied to routing problems,
Solving optimal control problems using dynamic programming,
Discrete linear regulator problem, Hamilton -Jacobi -Bellman Equation,
Numerical Techniques to determine optimal trajectories.

**ELL705 Stochastic Filtering and Identification (3-0-0)**

MMSE estimation including LMS, Gaussian case. Wiener filtering &
prediction. Kalman filtering & prediction. Extended Kalman filtering.
Predictors for difference equation based models including ARMA, Box
Jenkins & others. Statistical properties of Least Squares estimation
and its relationship with Bayes estimation (ML, MAP), convergence
analysis, CR bound. Recursive Least Squares, Iterative methods for
nonlinear Least Squares. Identification problem: Different approaches
for linear dynamical systems. Offline identification methods including
Least Squares, Prediction error framework, Pseudo-linear regression
(PLR) & Instrument variable methods. Recursive Identification of
linear dynamical system: RLS, PLR, Prediction error framework &
its application to ARMA & Innovations representation. Convergence
Analysis of Recursive Identification methods: Associated ODE,
Martingale. Nonlinear system identification. Subspace based method of
system identification. Applications including LQG and adaptive control.

**Program Elective Courses :**

**ELL704 Advanced Robotics (3-0-0)**

Review of Coordinate Transformations, D-H parameters and kinematics.
Velocity kinematics and Jacobian, Singularity analysis, Robot Dynamics.
Motion planning, Robot control: linear methods - feedforward control,
state feedback, observers; Nonlinear Control methods - Computed
Torque Control, Feedback linearization, Sliding Mode control; Vision
based Robotic Control. Holonomic and Non-Holonomic Systems,
Mobile Robots: Modeling and Control, Odometry Analysis, Navigation
problems with obstacle avoidance, motion capturing systems.

**ELL707 Systems Biology (3-0-0)**

MODELS : Variables and parameters, Law of mass action,
Representations : Deterministic vs stochastic, Spatial aspects,
Examples of core processes: Gene expression, Protein degradation,
Phosphorylation.

DYNAMICS : Equilibrium solutions, Bifurcations, Switches, Bistability,
Pulses and Oscillations, Circadian Rhythms and Clocks, Spatial
patterns. Morphogenesis and Development.

CONTROL MECHANISMS : Performance Goals, Integral Feedback
Control, Homeostasis and Perfect Adaptation, Bacterial Chemotaxis,
Feedforward Loops, Fold Change Detection, Robustness to
Perturbations, Tradeoffs, Internal Model Principle.

**ELL708 Selected Topics in Systems and Control (3-0-0)**

To be decided by the Instructor when floating this course: It can be
anything that is related to systems and control engineering, but is
not covered in any of the established courses.

**ELL709 Design Aspects in Control (3-0-0)**

System Modeling - model structures (Process model, ARX model),
Review of concepts of stability, feedback and feedforward control.
Classical control - First-Order Plus Dead-Time model (FOPDT), process
reaction curves, Second-Order Plus Dead-Time model (SOPDT), relay
feedback process identification; Smith Predictor and its variations, PID
controllers and their tuning, Ziegler-Nichols and Cohen-Coon techniques.
Reliable State Feedback design - pole placement, eigenstructure
assignment, region based eigenvalue assignment, eigenstructure-time
response relationships. Controller gain selection - noise sensitivity.
Controller robustness. Disturbance rejection. Frequency Domain Loop
Shaping. Output feedback control - compensator design, review of
Lead, Lag and Lag-Lead compensators, Zero dynamics - significance
in servo control design, design for unstable zero dynamics. Observers
- concept and design philosophy. Applications in practical controller
design scenarios.

**ELL800 Numerical Linear Algebra and Optimization in Engineering (3-0-0)**

Basics of Linear Algebra; Matrix decomposition - LU, LDU, QR and
Cholesky factorization; Householder reflection, Givens rotation;
Numerical implications of SVD; Numerical Solution for Linear Systems;
Algorithm Stability; Problem Conditioning; Pivoting and scaling; Least
Square Solutions; Numerical Matrix eigenvalue methods; Sparse
Systems; Iterative methods for large systems; Krylov, Arnoldi, Lanczos
methods; Numerical Optimization techniques - Conjugate gradient
method, Linear and quadratic programming, Spectral and Pseudo-spectral methods.

**ELL801 Nonlinear Control (3-0-0)**

Overview of nonlinear control, Lyapunov stability for autonomous
and non-autonomous systems, Input-Output Stability and Input-to-
State Stability, Passivity analysis and applications, Absolute Stability,
Incremental stability analysis, Lyapunov-based feedback control
design, Feedback linearization and backstepping, Sliding mode control,
Nonlinear observer design

**ELL802 Adaptive and Learning Control (3-0-0)**

Introduction to adaptive control, Review of Lyapunov stability theory,
Direct and indirect adaptive control, Model reference adaptive
control, Parameter convergence, persistence of excitation, Adaptive
backstepping, Adaptive control of nonlinear systems, Composite
adaptation, Neural Network-based control, Repetitive learning control,
Reinforcement learning-based control, Predictive control, Robust
adaptive control.

**ELL803 Model Reduction in Control (3-0-0)**

Introduction to Model Reduction; Sources of Large Models - Circuits,
Electromagnetic Systems, Mechanical Systems; Discretization Methods
- Finite Difference Method (FDM), Finite Element Method (FEM);
Classical Model Reduction Methods - Pade Approximation, Moment
matching, Routh Approximants; Modern Methods - Modal Model
Reduction Methods, SVD (Grammian) based methods, Krylov based
methods, SVD-Krylov based methods; MOR for Nonlinear Systems
- SVD & POD Methods; Model Reduction in Control; Control Design
on Reduced Models - Sub- optimal control; Sliding Mode Control as
model reducing control - First Order SM, Higher Order Sliding Mode.

**ELL804 Robust Control (3-0-0)**

Modeling of uncertain systems, Signals and Norms, Lyapunov theory
for LTI systems

Passive systems - frequency domain, Passive systems - time domain,
Robust Stability and performance, Stabilizing controllers - Coprime
factorization, LQR, LQG problems

Ricatti equations and solutions, H-infinity control and mu-synthesis,
Linear matrix inequalities for robust control, Ricatti equation solution
through LMI.

**ELL805 Networked and Multi-Agent Control Systems (3-0-0)**

Overview of networked systems, Graph Theory Fundamentals, Graph-
based Network Models, Network Optimization, Consensus Problem:
cooperative control, leader-follower architecture.

Control under Communication Constraints, Formation Control,
Swarming and Flocking Collision Avoidance, Game Theoretic Control
of Multi-Agent Systems, Applications: Multi-robot/vehicle coordination,
Sensor Networks, Social Networks, Smart Grids, Biological Networks.

**ELL806 Modeling and Control of Distributed Parameter Systems (3-0-0)**

Overview of networked systems, Graph Theory Fundamentals, Graph-
based Network Models, Network Optimization, Consensus Problem:
cooperative control, leader-follower architecture.

Control under Communication Constraints, Formation Control,
Swarming and Flocking Collision Avoidance, Game Theoretic Control
of Multi-Agent Systems, Applications: Multi-robot/vehicle coordination,
Sensor Networks, Social Networks, Smart Grids, Biological Networks.

**ELL807 Stochastic Control (3-0-0)**

Overview of stochastic systems with examples, Modeling of Stochastic
Systems: Continuous and discrete-time models subjected to noise,
Markov Decision Processes, Introduction to Stochastic Calculus and
Stochastic Differential Equations, Stochastic Stability, Stochastic
Optimal Control with complete and partial observations, finite and
infinite horizon problems, Linear and nonlinear Filtering, Separation
Principle, Linear quadratic Gaussian Problem, Stochastic Dynamic
Programming, Stochastic Adaptive Control, Applications: Finance,
operations research, biology.

**ELL808 Advanced Topics in Systems and Control (3-0-0)**

To be decided by the Instructor when floating this course: Can be
anything that is related to systems and control engineering but is not
covered in any of the established courses.